The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.
In this paper, we study the boundedness and estimate the essential norm of the differences of weighted composition operators from mixed-norm spaces to weighted-type spaces on the unit ball of CN.
The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space....The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.展开更多
Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this...Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this process is highly nonlinear and ill-posed,therefore achieving high-resolution imaging of complex biological tissues within a limited number of iterations remains challenging.We propose a multiscale frequency–domain full waveform inversion(FDFWI)framework for ultrasound computed tomography(USCT)imaging of biological tissues,which innovatively incorporates Sobolev space norm regularization for enhancement of prior information.Specifically,we investigate the effect of different types of hyperparameter on the imaging quality,during which the regularization weight is dynamically adapted based on the ratio of the regularization term to the data fidelity term.This strategy reduces reliance on predefined hyperparameters,ensuring robust inversion performance.The inversion results from both numerical and experimental tests(i.e.,numerical breast,thigh,and ex vivo pork-belly tissue)demonstrate the effectiveness of our regularized FWI strategy.These findings will contribute to the application of the FWI technique in quantitative imaging based on USCT and make USCT possible to be another high-resolution imaging method after x-ray computed tomography and magnetic resonance imaging.展开更多
In this paper, we characterize the boundedness and compactness of the weighted composi- tion operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the...In this paper, we characterize the boundedness and compactness of the weighted composi- tion operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators.展开更多
In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q((?)1),Hu,v((?)2)) for the values of p, q, u, v in three cases: (i)0<p≤u≤∞, 0 < q≤min(1,v)≤frr. (ii) v =∞,0<p≤...In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q((?)1),Hu,v((?)2)) for the values of p, q, u, v in three cases: (i)0<p≤u≤∞, 0 < q≤min(1,v)≤frr. (ii) v =∞,0<p≤u≤∞, 1≤u, q≤∞. (iii) 1≤v≤2≤q≤∞, and 0<p≤u≤∞or 1≤p, u≤∞. The first case extends the result of Blasco, Jevtic, and Pavlovic in one variable. The third case generalizes partly the results of Jevtic, Jovanovic, and Wojtaszczyk to higher dimensions.展开更多
Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,...Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,q, φ ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ（B）. The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.展开更多
Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of...Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.展开更多
Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk...Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.展开更多
Let Bp^n={x∈R^b｜‖x‖p≤1} be the unit ball of p norm in the n-dimensional normed space εp＆n.The formula for the volume of Bp^n was obtained and its asymptotic properties were found out as n→∞and p→∞.
Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω...Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω, a, Hp,q,) is solvable for any fixed point a ∈ Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on Hp,q,.展开更多
In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of t...In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.展开更多
It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially norm...It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially normed spaces are given.展开更多
The best approximation, best Σ approximation and best sup approximation in linear 2 normed spaces are discussed in this paper. The characterization and uniqueness theorems for these nonlinear approximations are gi...The best approximation, best Σ approximation and best sup approximation in linear 2 normed spaces are discussed in this paper. The characterization and uniqueness theorems for these nonlinear approximations are given.展开更多
In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessar...In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessary conditions were given for the extreme point of Orlicz-Bochner sequence space and the conditions in part for Orlicz-Bochner function space.展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.展开更多
The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive m...The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.展开更多
The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of no...The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.展开更多
In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kern...In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kernel of elementary operators and the operators implementing them also are given.展开更多
基金item： Supported by the National Natural Science Foundation of China（60573040）
文摘The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 1097115310671141)
文摘In this paper, we study the boundedness and estimate the essential norm of the differences of weighted composition operators from mixed-norm spaces to weighted-type spaces on the unit ball of CN.
文摘The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.
基金supported by the National Natural Science Foundation of China(Grant No.12474461)the Basic and Frontier Exploration Project Independently Deployed by Institute of Acoustics,Chinese Academy of Sciences(Grant No.JCQY202402)the Goal-Oriented Project Independently Deployed by Institute of Acoustics,Chinese Academy of Sciences(Grant No.MBDX202113).
文摘Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this process is highly nonlinear and ill-posed,therefore achieving high-resolution imaging of complex biological tissues within a limited number of iterations remains challenging.We propose a multiscale frequency–domain full waveform inversion(FDFWI)framework for ultrasound computed tomography(USCT)imaging of biological tissues,which innovatively incorporates Sobolev space norm regularization for enhancement of prior information.Specifically,we investigate the effect of different types of hyperparameter on the imaging quality,during which the regularization weight is dynamically adapted based on the ratio of the regularization term to the data fidelity term.This strategy reduces reliance on predefined hyperparameters,ensuring robust inversion performance.The inversion results from both numerical and experimental tests(i.e.,numerical breast,thigh,and ex vivo pork-belly tissue)demonstrate the effectiveness of our regularized FWI strategy.These findings will contribute to the application of the FWI technique in quantitative imaging based on USCT and make USCT possible to be another high-resolution imaging method after x-ray computed tomography and magnetic resonance imaging.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10971153, 10671141)
文摘In this paper, we characterize the boundedness and compactness of the weighted composi- tion operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10471134)grants from Specialized Research Fund for the doctoral program of Higher Education(SRFDP20050358052)Program for New Century Excellent Talents in University(NCET-05-0539).
文摘In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q((?)1),Hu,v((?)2)) for the values of p, q, u, v in three cases: (i)0<p≤u≤∞, 0 < q≤min(1,v)≤frr. (ii) v =∞,0<p≤u≤∞, 1≤u, q≤∞. (iii) 1≤v≤2≤q≤∞, and 0<p≤u≤∞or 1≤p, u≤∞. The first case extends the result of Blasco, Jevtic, and Pavlovic in one variable. The third case generalizes partly the results of Jevtic, Jovanovic, and Wojtaszczyk to higher dimensions.
基金Supported by the NNSF of China (10771064,10971063)the NSF of Zhejiang Province (Y6100219, Y7080197, Y6090036, D7080080)the Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924)
文摘Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,q, φ ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ（B）. The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.
基金supported by the National Natural Science Foundation of China(Nos.11101139,11271124)the Natural Science Foundation of Zhejiang Province(Nos.Y6090036,Y6100219)the Foundation of Creative Group in Universities of Zhejiang Province(No.T200924)
文摘Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.
文摘Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.
基金Project supported by the Science Foundation of Shanghai Municipal Commission of Education (Grant No.24667).
文摘Let Bp^n={x∈R^b｜‖x‖p≤1} be the unit ball of p norm in the n-dimensional normed space εp＆n.The formula for the volume of Bp^n was obtained and its asymptotic properties were found out as n→∞and p→∞.
基金supported by the 151 Projetion and the Natural Science Foundation of Zhejiang Province.
文摘Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω, a, Hp,q,) is solvable for any fixed point a ∈ Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on Hp,q,.
基金supported by the Natural Science Foundation of Yibin University (No. 2009Z003)
文摘In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.
文摘It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially normed spaces are given.
文摘The best approximation, best Σ approximation and best sup approximation in linear 2 normed spaces are discussed in this paper. The characterization and uniqueness theorems for these nonlinear approximations are given.
文摘In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessary conditions were given for the extreme point of Orlicz-Bochner sequence space and the conditions in part for Orlicz-Bochner function space.
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
文摘The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.
基金supported by the Natural Science Foundation of Yibin University(No.2009Z03)
文摘The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.
基金National Council for Science and Technology (NCST) of KenyaDAAD-Germany for the financial support
文摘In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kernel of elementary operators and the operators implementing them also are given.
