In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on...In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.展开更多
The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. ...The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.展开更多
In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lo...In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lorentz spaces are proved.展开更多
In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
Low-frequency oscillations(LFOs)in traction power supply systems(TPSSs)frequently arise when multiple electric trains simultaneously raise their panto-graphs under the same power supply arm.This phenomenon is characte...Low-frequency oscillations(LFOs)in traction power supply systems(TPSSs)frequently arise when multiple electric trains simultaneously raise their panto-graphs under the same power supply arm.This phenomenon is characterized by low-frequency fluctuations(2-8 Hz)in the envelope waveforms of traction network voltage and current.It can lead to operational issues such as insufficient current acquisition and difficulties in depot entry or exit,thereby adversely affecting railway operations.Given the time-varying nature of LFOs,timely and accurate detection is critical for implementing effective mitigation strategies,with faster detection enabling improved outcomes.This paper proposes a real-time detection algorithm for LFOs in AC traction networks that integrates signal preprocessing,spectral analysis,and parameter optimization.First,the voltage signal is pro-cessed using a low-pass filter to suppress high-frequency noise.Then,a fast Fourier transform(FFT)-based spectral estimation method is applied to extract frequen-cy-domain features.Oscillation parameter identification is triggered when the identified signal amplitude exceeds predefined thresholds in the 42-48 Hz and 52-58 Hz bands.Subsequently,during the identification stage,an LFO atom dictionary is constructed based on the FFT pre-analysis results.Finally,the matching pursuit algorithm is employed to achieve fast and accurate extraction of LFO parameters.The proposed method is validated using both simulated and real-world measurement data.Experimental results confirm its effectiveness in detecting LFOs under noisy conditions,demonstrating high accuracy and computational efficiency.The approach provides valuable insights for the threshold selection of protection devices,thereby enhancing the stability and reliability of TPSSs.展开更多
In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms.They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory.And then three atomic decomp...In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms.They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory.And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved.With the help of the weak atomic decompositions of martingale,a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given.Using the sufficient condition,we obtain a series of martingale inequalities with respect to the weak L_(p)-norm,the inequalities of weak(p,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces.These inequalities are the weak versions of the basic inequalities in the classical martingale H_(p)-theory.展开更多
Some atomic decomposition theorems for Banach-space-valued martingales are established.Using them,the embedding relationships between martingale spaces with small index are discussed.The results obtained here are conn...Some atomic decomposition theorems for Banach-space-valued martingales are established.Using them,the embedding relationships between martingale spaces with small index are discussed.The results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of Banach space in which the martingales take values.展开更多
The main purpose of this paper is to derive a new （p,q）-atomic decomposition on the multi-parameter Hardy space HP（X1 × X2） for 0 〈 po 〈 P ≤ 1 for some po and all 1 〈 q 〈 ∞, where X1 ×X2 is the pro...The main purpose of this paper is to derive a new （p,q）-atomic decomposition on the multi-parameter Hardy space HP（X1 × X2） for 0 〈 po 〈 P ≤ 1 for some po and all 1 〈 q 〈 ∞, where X1 ×X2 is the product of two spaces of homogeneous type in the sense of Coifman and Weiss. This decomposition converges in both L^q（X1 × X2） （for 1 〈 q 〈 ∞） and Hardy space HP（X1× X2） （for 0 〈 p _〈 1）. As an application, we prove that an operator T, which is bounded on Lq（X1× X2） for some 1 〈 q 〈 ∞, is bounded from H^p（X1 × X2） to L^p（X1 × X2） if and only if T is bounded uniformly on all （p, q）-product atoms in LP（X1 × X2）. The similar boundedness criterion from HP（X1 × X2） to HP（X1 × X2） is also obtained.展开更多
We introduce the weak Hardy-Morrey spaces in this paper.We also obtain the atomic decompositions of the weak Hardy-Morrey spaces.By using these decompositions,we establish the Hardy inequalities on the weak Hardy-Morr...We introduce the weak Hardy-Morrey spaces in this paper.We also obtain the atomic decompositions of the weak Hardy-Morrey spaces.By using these decompositions,we establish the Hardy inequalities on the weak Hardy-Morrey spaces.展开更多
Let w E Am. In this paper, we introduce weighted-（p,q） atomicHardy spaces Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw and show that the weighted Hardy space Hwp（Rn × Rm） defined via Littlewood-Paley square...Let w E Am. In this paper, we introduce weighted-（p,q） atomicHardy spaces Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw and show that the weighted Hardy space Hwp（Rn × Rm） defined via Littlewood-Paley square functions coincides with Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw. As applications, we get a general principle on the Hwp（Rn × Rm to Lwp（Rn × Rm） boundedness and a boundedness criterion for two parameter singular integrals on the weighted Hardy spaces.展开更多
In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the e...In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level.The authors obtain the finite atomic decomposition characterization of Hardy spaces H^(p)(Θ)and as an application,the authors prove that given an admissible triplet(p,q,l)with 1≤q≤∞,if T is a sublinear operator and uniformly bounded elements of some quasi-Banach space B for maps all(p,q,l)-atoms with q<∞(or all continuous(p,q,l)-atoms with q=∞),then T uniquely extends to a bounded sublinear operator from H^(p)(Θ)to B.These results generalize the known results on the anisotropic Hardy spaces of Bownik et al.展开更多
In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale in...In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.展开更多
Cementites decomposition of a pearlitic ductile cast iron during graphitization annealing heat treatment was investigated.Fractographies and microstructures of heat treated samples were observed using a scanning elect...Cementites decomposition of a pearlitic ductile cast iron during graphitization annealing heat treatment was investigated.Fractographies and microstructures of heat treated samples were observed using a scanning electron microscope and mechanical properties were measured by a universal tensile test machine.The results indicated that during isothermal annealing at 750°C,the tensile strength of pearlitic ductile cast iron was increased to a peak value at 0.5h,and decreased gradually thereafter but the elongation was enhanced with the increase of annealing time.Moreover,the diffusion coefficient of carbon atoms could be approximately calculated as 0.56μm2/s that could be regarded as the shortrange diffusion.As the holding time was short（0.5h）,diffusion of carbon atoms was incomplete and mainly occurred around the graphites where the morphology of cementites changed from fragmentized shape to granular shape.In addition,the ductile cast iron with tensile strength of 740MPa and elongation of 7% could be achieved after graphitization annealing heat treatment for 0.5h.Two principal factors should be taken into account.First,the decomposition of a small amount of cementites was beneficial for increasing the ductility up to elongation of 7%.Second,the diffusion of carbon atoms from cementites to graphites could improve the binding force between graphites and matrix,enhancing the tensile strength to 740 MPa.展开更多
Let 0<p≤1<q<∞,andω1,ω2 E A1(Muckenhoupt-class).We study an oscillating multiplier operator Tγ,βand obtain that it is boundedon the homogeneous weighted Herz-type Hardy spaces HK_(q)^(α,p)(R^(n);ω1,ω2...Let 0<p≤1<q<∞,andω1,ω2 E A1(Muckenhoupt-class).We study an oscillating multiplier operator Tγ,βand obtain that it is boundedon the homogeneous weighted Herz-type Hardy spaces HK_(q)^(α,p)(R^(n);ω1,ω2)whenγ=nβ/2,α=n(1-1/q).Also,for the unweighted case,we obtain the Hk_(q)^(α,p)(R^(n))boundedness of Tγ,βunder certain conditions on y.These results are substantial improvements and extensions of the main results in the papers by Li and Lu and by Cao and Sun.As an application,we prove the HK_(q)^(α,p)(R^(n))boundedness of the spherical average S_(t)^(δ)uniformly on t>0.展开更多
We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function ...We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.展开更多
In this paper we introduce the concept of two-parameterB-valued strong martingales and investigate some features of these strong martingales. We also characterizep-smoothable Banach spaces in terms of these strong mar...In this paper we introduce the concept of two-parameterB-valued strong martingales and investigate some features of these strong martingales. We also characterizep-smoothable Banach spaces in terms of these strong martingales.展开更多
To suppress noise amplitude modulation jamming in a single-antenna radar system, a new method based on weighted-matching pursuit （WMP） algorithm is proposed, which can achieve underdetermined blind sources separatio...To suppress noise amplitude modulation jamming in a single-antenna radar system, a new method based on weighted-matching pursuit （WMP） algorithm is proposed, which can achieve underdetermined blind sources separation of the jamming and the target echo from the jammed mixture in the single channel of the receiver. Firstly, the presented method utilizes a prior information about the differences between the jamming component and the radar transmitted signal to construct two signal-adapted sub-dictionaries and to determine the weights. Then the WMP algorithm is applied to remove the jamming component from the mixture. Experimental results verify the validity of the presented method. By comparison of the pulse compression performance, the simulation results shows that the presented method is superior to the method of frequency domain cancellation （FDC） when the jamming-to-signal ratio （JSR） is lower than 15 dB.展开更多
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Trieb...For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp^0,q （1 〈 p,q 〈 ∞） and on a party of endpoint spaces FO,q （1 ≤ q ≤ 2）, hut this idea is invalid for endpoint Triebel-Lizorkin spaces F1^0,q （2 〈 q ≤ ∞）. In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F1^0,q （2 〈 q ≤ ∞） under an integrable condition which approaches HSrmander condition infinitely.展开更多
基金Supported by the National Natural Foundation of China(10671147)
文摘In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.
基金supported by the Education Department Important Foundation of Hunan Province in China(10A074)supported by the Education Department Important Foundation of Hunan Provincein China(12A206)College of Mathematics and Computer Science,Key Laboratory of High Performance Computing and Stochastic Information Processing(Ministry of Education of China),Hunan Normal University,and the Construct Program of the Key Discipline in Hunan Province
文摘Let μ be a normal function on [0, 1）. The atomic decomposition of the μ-Bergman space in the unit ball B is given for all p 〉 0.
基金Supported by the National Natural Science Foun-dation of China (10371093)
文摘The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.
基金supported by the National Natural Science Foundation of China(10871016)
文摘In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lorentz spaces are proved.
基金Sponsored by the National NSFC under grant No.19771063
文摘In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
基金supported by the National Natural Sci-ence Foundation of China(No.52472420)the Fundamental Research Funds for the Central Universi-ties(No.2682024CX081).
文摘Low-frequency oscillations(LFOs)in traction power supply systems(TPSSs)frequently arise when multiple electric trains simultaneously raise their panto-graphs under the same power supply arm.This phenomenon is characterized by low-frequency fluctuations(2-8 Hz)in the envelope waveforms of traction network voltage and current.It can lead to operational issues such as insufficient current acquisition and difficulties in depot entry or exit,thereby adversely affecting railway operations.Given the time-varying nature of LFOs,timely and accurate detection is critical for implementing effective mitigation strategies,with faster detection enabling improved outcomes.This paper proposes a real-time detection algorithm for LFOs in AC traction networks that integrates signal preprocessing,spectral analysis,and parameter optimization.First,the voltage signal is pro-cessed using a low-pass filter to suppress high-frequency noise.Then,a fast Fourier transform(FFT)-based spectral estimation method is applied to extract frequen-cy-domain features.Oscillation parameter identification is triggered when the identified signal amplitude exceeds predefined thresholds in the 42-48 Hz and 52-58 Hz bands.Subsequently,during the identification stage,an LFO atom dictionary is constructed based on the FFT pre-analysis results.Finally,the matching pursuit algorithm is employed to achieve fast and accurate extraction of LFO parameters.The proposed method is validated using both simulated and real-world measurement data.Experimental results confirm its effectiveness in detecting LFOs under noisy conditions,demonstrating high accuracy and computational efficiency.The approach provides valuable insights for the threshold selection of protection devices,thereby enhancing the stability and reliability of TPSSs.
基金supported by National Natural Science Foundation of China(Grant No.10371093).
文摘In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms.They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory.And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved.With the help of the weak atomic decompositions of martingale,a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given.Using the sufficient condition,we obtain a series of martingale inequalities with respect to the weak L_(p)-norm,the inequalities of weak(p,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces.These inequalities are the weak versions of the basic inequalities in the classical martingale H_(p)-theory.
基金the National Natural Science Foundation of China(Grant No.10071059).
文摘Some atomic decomposition theorems for Banach-space-valued martingales are established.Using them,the embedding relationships between martingale spaces with small index are discussed.The results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of Banach space in which the martingales take values.
文摘The main purpose of this paper is to derive a new （p,q）-atomic decomposition on the multi-parameter Hardy space HP（X1 × X2） for 0 〈 po 〈 P ≤ 1 for some po and all 1 〈 q 〈 ∞, where X1 ×X2 is the product of two spaces of homogeneous type in the sense of Coifman and Weiss. This decomposition converges in both L^q（X1 × X2） （for 1 〈 q 〈 ∞） and Hardy space HP（X1× X2） （for 0 〈 p _〈 1）. As an application, we prove that an operator T, which is bounded on Lq（X1× X2） for some 1 〈 q 〈 ∞, is bounded from H^p（X1 × X2） to L^p（X1 × X2） if and only if T is bounded uniformly on all （p, q）-product atoms in LP（X1 × X2）. The similar boundedness criterion from HP（X1 × X2） to HP（X1 × X2） is also obtained.
文摘We introduce the weak Hardy-Morrey spaces in this paper.We also obtain the atomic decompositions of the weak Hardy-Morrey spaces.By using these decompositions,we establish the Hardy inequalities on the weak Hardy-Morrey spaces.
文摘Let w E Am. In this paper, we introduce weighted-（p,q） atomicHardy spaces Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw and show that the weighted Hardy space Hwp（Rn × Rm） defined via Littlewood-Paley square functions coincides with Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw. As applications, we get a general principle on the Hwp（Rn × Rm to Lwp（Rn × Rm） boundedness and a boundedness criterion for two parameter singular integrals on the weighted Hardy spaces.
基金Supported by the Xinjiang Training of Innovative Personnel Natural Science Foundation of China(Grant No.2020D01C048)the National Natural Science Foundation of China(Grant No.11861062)。
文摘In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level.The authors obtain the finite atomic decomposition characterization of Hardy spaces H^(p)(Θ)and as an application,the authors prove that given an admissible triplet(p,q,l)with 1≤q≤∞,if T is a sublinear operator and uniformly bounded elements of some quasi-Banach space B for maps all(p,q,l)-atoms with q<∞(or all continuous(p,q,l)-atoms with q=∞),then T uniquely extends to a bounded sublinear operator from H^(p)(Θ)to B.These results generalize the known results on the anisotropic Hardy spaces of Bownik et al.
基金Supported by the National Natural Science Foundation of China(11871195)。
文摘In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.
基金supported by the Program for Innovative Research Team in University of Liaoning Province(Grant No.LT2015020)National Natural Science Foundation of China(Grant No.51274142)
文摘Cementites decomposition of a pearlitic ductile cast iron during graphitization annealing heat treatment was investigated.Fractographies and microstructures of heat treated samples were observed using a scanning electron microscope and mechanical properties were measured by a universal tensile test machine.The results indicated that during isothermal annealing at 750°C,the tensile strength of pearlitic ductile cast iron was increased to a peak value at 0.5h,and decreased gradually thereafter but the elongation was enhanced with the increase of annealing time.Moreover,the diffusion coefficient of carbon atoms could be approximately calculated as 0.56μm2/s that could be regarded as the shortrange diffusion.As the holding time was short（0.5h）,diffusion of carbon atoms was incomplete and mainly occurred around the graphites where the morphology of cementites changed from fragmentized shape to granular shape.In addition,the ductile cast iron with tensile strength of 740MPa and elongation of 7% could be achieved after graphitization annealing heat treatment for 0.5h.Two principal factors should be taken into account.First,the decomposition of a small amount of cementites was beneficial for increasing the ductility up to elongation of 7%.Second,the diffusion of carbon atoms from cementites to graphites could improve the binding force between graphites and matrix,enhancing the tensile strength to 740 MPa.
基金supported by the National Key Research and Development Program of China(22YFA10057001)the National Science Foundation of Guangdong Province(2023A1515012034)the National Natural Science Foundation of China(12371105,11971295).
文摘Let 0<p≤1<q<∞,andω1,ω2 E A1(Muckenhoupt-class).We study an oscillating multiplier operator Tγ,βand obtain that it is boundedon the homogeneous weighted Herz-type Hardy spaces HK_(q)^(α,p)(R^(n);ω1,ω2)whenγ=nβ/2,α=n(1-1/q).Also,for the unweighted case,we obtain the Hk_(q)^(α,p)(R^(n))boundedness of Tγ,βunder certain conditions on y.These results are substantial improvements and extensions of the main results in the papers by Li and Lu and by Cao and Sun.As an application,we prove the HK_(q)^(α,p)(R^(n))boundedness of the spherical average S_(t)^(δ)uniformly on t>0.
基金Supported by the National Natural Science Foundation of China(10931001, 10871173 and 11026104)
文摘We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.
文摘In this paper we introduce the concept of two-parameterB-valued strong martingales and investigate some features of these strong martingales. We also characterizep-smoothable Banach spaces in terms of these strong martingales.
文摘To suppress noise amplitude modulation jamming in a single-antenna radar system, a new method based on weighted-matching pursuit （WMP） algorithm is proposed, which can achieve underdetermined blind sources separation of the jamming and the target echo from the jammed mixture in the single channel of the receiver. Firstly, the presented method utilizes a prior information about the differences between the jamming component and the radar transmitted signal to construct two signal-adapted sub-dictionaries and to determine the weights. Then the WMP algorithm is applied to remove the jamming component from the mixture. Experimental results verify the validity of the presented method. By comparison of the pulse compression performance, the simulation results shows that the presented method is superior to the method of frequency domain cancellation （FDC） when the jamming-to-signal ratio （JSR） is lower than 15 dB.
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
基金Sponsored by the NSF of South-Central University for Nationalities (YZZ08004)the Doctoral programme foundation of National Education Ministry of China
文摘For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp^0,q （1 〈 p,q 〈 ∞） and on a party of endpoint spaces FO,q （1 ≤ q ≤ 2）, hut this idea is invalid for endpoint Triebel-Lizorkin spaces F1^0,q （2 〈 q ≤ ∞）. In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F1^0,q （2 〈 q ≤ ∞） under an integrable condition which approaches HSrmander condition infinitely.
