This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from...This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.展开更多
Inhomogeneous Calderon-Zygmund operator T maps each atom into an approximate molecule of weighted local Hardy space if and only if some approximate cancellation condition holds for T.An equivalent norm for weighted Le...Inhomogeneous Calderon-Zygmund operator T maps each atom into an approximate molecule of weighted local Hardy space if and only if some approximate cancellation condition holds for T.An equivalent norm for weighted Lebesgue space which has vanishing moments up to order s plays an important role,where s∈N.展开更多
Le be a nonnegative Radon measure on Rd which satisfies the growth condition （B（x, r）） Cotfor all x E Rd and r 〉 O, where Co is a fixed constant and 0 〈 n d. The purpose of this paper is to establish the boun...Le be a nonnegative Radon measure on Rd which satisfies the growth condition （B（x, r）） Cotfor all x E Rd and r 〉 O, where Co is a fixed constant and 0 〈 n d. The purpose of this paper is to establish the boundedness of the Marcinkiewicz integrals from LP（u） to LP（u）, where u is a weight function of Muckenhoupt type associated with ~.展开更多
In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey ...In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weight and variable exponent, which essentially extend some known results.展开更多
Let 0 〈 p ≤ 1 and w in the Muckenhoupt class A1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and yang[11] established that the Riesz transforms R j, j = 1,2,..., n, ...Let 0 〈 p ≤ 1 and w in the Muckenhoupt class A1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and yang[11] established that the Riesz transforms R j, j = 1,2,..., n, are bounded on Hwp （Rn）. In this note we extend this to the general case of weight w in the Muckenhoupt class A.. through molecular characterization. One difficulty, which has not been taken care in [11] consists in passing from atoms to all functions in HwP（Rn）. Furthermore, the HwP-boundedness of θ- Calderon-Zygmund operators are also given through molecular characterization and atomic decomposition.展开更多
Let T be an anisotropic Calderón-Zygmund operator andφ:R^n×[0,∞)→[0,∞)be an anisotropic Musielak-Orlicz function withφ(x,·)being an Orlicz function andφ(·,t)being a Muckenhoupt A∞(A)weight.I...Let T be an anisotropic Calderón-Zygmund operator andφ:R^n×[0,∞)→[0,∞)be an anisotropic Musielak-Orlicz function withφ(x,·)being an Orlicz function andφ(·,t)being a Muckenhoupt A∞(A)weight.In this paper,our goal is to study two boundedness theorems for commutators of anisotropic Calderon-Zygmund operators.Precisely,when b∈BMOw(R^n,A)(a proper subspace of anisotropic bounded mean oscillation space BMO(R^n,A)),the commutator[b,T]is bounded from anisotropic weighted Hardy space H^1ω(R^n,A)to weighted Lebesgue space L^1ω(R^n)and when b∈BMO(R^n)(bounded mean oscillation space),the commutator[b,T]is bounded on Musielak-Orlicz space L^φ(R^n),which are extensions of the isotropic setting.展开更多
基金supported by the National Natural Science Foundation of China(11771379)the Natural Science Foundation of Jiangsu Province(BK20161326)+2 种基金the School Foundation of Yangzhou University(2016CXJ001)supported by the National Natural Science Foundation of China(11401525)the Natural Science Foundation of Zhejiang Province(LY18A010006)
基金supported by National Natural Science Foundation of China(Grant No.11661075)
文摘This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.
文摘Inhomogeneous Calderon-Zygmund operator T maps each atom into an approximate molecule of weighted local Hardy space if and only if some approximate cancellation condition holds for T.An equivalent norm for weighted Lebesgue space which has vanishing moments up to order s plays an important role,where s∈N.
基金Li Baode is supported by NSFC(No.11461065,No.11161044)Scientific Research Projects in Colleges and Universities in Xinjiang Uyghur Autonomous Region(No.XJEDU2014S001)
基金supported by the Natural Science Foundation of Xinjiang Uyghur Autonomous Region(2015211C283)
文摘设A是一个扩张矩阵,α∈[0,1),p∈(1,1/α)且q:=(1/p-α)-1,如果非负函数v满足各向异性的Muckenhoupt Ap,q(A)权条件,那么各向异性的分数次极大函数f*α从Lp(Rn,vp)到Lq(Rn,vq)是有界的.作为应用,作者进一步证明了v∈Ap,q(A)当且仅当各向异性分数次积分算子Tα,A从Lp(Rn,vp)到Lq(Rn,vq)是有界的,这些结论是Muckenhoupt和Wheeden的结果在各向异性情形下的推广(Trans Amer Math Soc,192:261-274,1974).
基金supported by the National Natural Science Foundation of China(11461065)Scientific Research Projects in Colleges and Universities in Xinjiang Uyghur Autonomous Region(XJEDU2014S001)
基金Supported by the National Natural Science Foundation of China(1146106511661075)a Cultivate Project for Young Doctor from Xinjiang Uyghur Autonomous Region(qn2015bs003)
基金Supported by the National Natural Science Foundation of China (Grant No. 10861010)
文摘Le be a nonnegative Radon measure on Rd which satisfies the growth condition （B（x, r）） Cotfor all x E Rd and r 〉 O, where Co is a fixed constant and 0 〈 n d. The purpose of this paper is to establish the boundedness of the Marcinkiewicz integrals from LP（u） to LP（u）, where u is a weight function of Muckenhoupt type associated with ~.
文摘In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weight and variable exponent, which essentially extend some known results.
文摘Let 0 〈 p ≤ 1 and w in the Muckenhoupt class A1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and yang[11] established that the Riesz transforms R j, j = 1,2,..., n, are bounded on Hwp （Rn）. In this note we extend this to the general case of weight w in the Muckenhoupt class A.. through molecular characterization. One difficulty, which has not been taken care in [11] consists in passing from atoms to all functions in HwP（Rn）. Furthermore, the HwP-boundedness of θ- Calderon-Zygmund operators are also given through molecular characterization and atomic decomposition.
基金supported by the “Basic Innovation” Program of Graduate Students of Guangzhou University(2018GDJC-D01)the second author is supported by the National Natural Science Foundation of China(11861062,11661075 and 11561065)the third author is supported by the the National Natural Science Foundation of China(11671414).
文摘Let T be an anisotropic Calderón-Zygmund operator andφ:R^n×[0,∞)→[0,∞)be an anisotropic Musielak-Orlicz function withφ(x,·)being an Orlicz function andφ(·,t)being a Muckenhoupt A∞(A)weight.In this paper,our goal is to study two boundedness theorems for commutators of anisotropic Calderon-Zygmund operators.Precisely,when b∈BMOw(R^n,A)(a proper subspace of anisotropic bounded mean oscillation space BMO(R^n,A)),the commutator[b,T]is bounded from anisotropic weighted Hardy space H^1ω(R^n,A)to weighted Lebesgue space L^1ω(R^n)and when b∈BMO(R^n)(bounded mean oscillation space),the commutator[b,T]is bounded on Musielak-Orlicz space L^φ(R^n),which are extensions of the isotropic setting.
