We consider the convolution transforms of measures on R<sup>d</sup> defined by some approximate identity. We shall establish some relations between the irregular boundary properties of the convolution func...We consider the convolution transforms of measures on R<sup>d</sup> defined by some approximate identity. We shall establish some relations between the irregular boundary properties of the convolution function and the local Lipschitz exponent of the measure. In particular, the results can be applied to the Poisson and Gauss-Weierstrass kernels. We can then obtain some singular boundary behavior of positive harmonic or parabolic functions on R<sub>+</sub><sup>d+1</sup> by multifractal analysis of measures.展开更多
This study introduces a pre-orthogonal adaptive Fourier decomposition(POAFD)to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli an...This study introduces a pre-orthogonal adaptive Fourier decomposition(POAFD)to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre(generalized Poisson equation).As a first step,the method expands the initial data function into a sparse series of the fundamental solutions with fast convergence,and,as a second step,makes use of the semigroup or the reproducing kernel property of each of the expanding entries.Experiments show the effectiveness and efficiency of the proposed series solutions.展开更多
The aim of this paper is to set up the weighted norm inequalities for commutators generated by approximate identities from weighted Lebesgue spaces into weighted Morrey spaces
Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper ty...Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper type 1 and lower type p ∈（0,1].In this article,the authors introduce a new Musielak–Orlicz BMO-type space BMOψA（X） associated with the generalized approximation to the identity,give out its basic properties and establish its two equivalent characterizations,respectively,in terms of the spaces BMOψA,max（X） and BMOψA（X）.Moreover,two variants of the John–Nirenberg inequality on BMOψA（X） are obtained.As an application,the authors further prove that the space BMOψΔ1/2（Rn）,associated with the Poisson semigroup of the Laplace operator Δ on Rn,coincides with the space BMOψ（Rn） introduced by Ky.展开更多
In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 （Rn） ×..…… L1 （Rn） to L1/m,...In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 （Rn） ×..…… L1 （Rn） to L1/m,∞（Rn）, and the associated kernel K（x; yl,.. , Ym） enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.展开更多
By sharp maximal function, we establish a weighted estimate with multiple-weight for the multilinear singular integral operators with non-smooth kernels.
文摘We consider the convolution transforms of measures on R<sup>d</sup> defined by some approximate identity. We shall establish some relations between the irregular boundary properties of the convolution function and the local Lipschitz exponent of the measure. In particular, the results can be applied to the Poisson and Gauss-Weierstrass kernels. We can then obtain some singular boundary behavior of positive harmonic or parabolic functions on R<sub>+</sub><sup>d+1</sup> by multifractal analysis of measures.
基金supported by the Science and Technology Development Fund of Macao SAR(FDCT0128/2022/A,0020/2023/RIB1,0111/2023/AFJ,005/2022/ALC)the Shandong Natural Science Foundation of China(ZR2020MA004)+2 种基金the National Natural Science Foundation of China(12071272)the MYRG 2018-00168-FSTZhejiang Provincial Natural Science Foundation of China(LQ23A010014).
文摘This study introduces a pre-orthogonal adaptive Fourier decomposition(POAFD)to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre(generalized Poisson equation).As a first step,the method expands the initial data function into a sparse series of the fundamental solutions with fast convergence,and,as a second step,makes use of the semigroup or the reproducing kernel property of each of the expanding entries.Experiments show the effectiveness and efficiency of the proposed series solutions.
基金supported by the NSF(11271175) of Chinathe NSF(ZR2012AQ026) of Shandong Province
文摘The aim of this paper is to set up the weighted norm inequalities for commutators generated by approximate identities from weighted Lebesgue spaces into weighted Morrey spaces
基金supported by National Natural Science Foundation of China(Grant Nos.11171027 and 11361020)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2012LYB26,2012CXQT09 and lzujbky-2014-18)
文摘Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper type 1 and lower type p ∈（0,1].In this article,the authors introduce a new Musielak–Orlicz BMO-type space BMOψA（X） associated with the generalized approximation to the identity,give out its basic properties and establish its two equivalent characterizations,respectively,in terms of the spaces BMOψA,max（X） and BMOψA（X）.Moreover,two variants of the John–Nirenberg inequality on BMOψA（X） are obtained.As an application,the authors further prove that the space BMOψΔ1/2（Rn）,associated with the Poisson semigroup of the Laplace operator Δ on Rn,coincides with the space BMOψ（Rn） introduced by Ky.
基金Supported by National Natural Science Foundation of China (Grant No. 10971228)
文摘In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 （Rn） ×..…… L1 （Rn） to L1/m,∞（Rn）, and the associated kernel K（x; yl,.. , Ym） enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11371316, 11271330, 11571306）.
文摘By sharp maximal function, we establish a weighted estimate with multiple-weight for the multilinear singular integral operators with non-smooth kernels.
