Riesz Potential and Maximal Function for Dunkl transform

被引：0
作者：
D. V. Gorbachev
V. I. Ivanov
S. Yu. Tikhonov
机构：
[1] Tula State University,Department of Applied Mathematics and Computer Science
[2] Centre de Recerca Matemàtica,undefined
[3] ICREA,undefined
[4] and Universitat Autònoma de Barcelona,undefined
来源：
Potential Analysis | 2021年 / 55卷
关键词：
Dunkl transform; Generalized translation operator; Convolution; Riesz potential; 42B10; 33C45; 33C52;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study weighted (Lp, Lq)-boundedness properties of Riesz potentials and fractional maximal functions for the Dunkl transform. In particular, we obtain the weighted Hardy–Littlewood–Sobolev type inequality and weighted week (L1, Lq) estimate. We find a sharp constant in the weighted Lp-inequality, generalizing the results of W. Beckner and S. Samko.
引用
收藏
页码：513 / 538
页数：25
相关论文
共 44 条
  • [1] Abdelkefi C(2015)Some properties of the Riesz potentials in Dunkl analysis Ricerche Mat. 4 195-215
  • [2] Rachdi M(2008)Pitt’s inequality with sharp convolution estimates Proc. Am. Math. Soc. 5 1871-1885
  • [3] Beckner W(1995)Best constants for two nonconvolution inequalities Proc. Am. Math. Soc. 6 1687-1693
  • [4] Christ M(1992)Hankel transforms associated to finite reflections groups Contemp. Math. 138 123-138
  • [5] Grafakos L(2012)Sharp bounds for m-linear Hardy and Hilbert operators Houst. J. Math. 1 225-244
  • [6] Dunkl CF(2011)The Stein–Weiss type inequalities for the B-Riesz potentials J. Math. Ineq. 5 87-106
  • [7] Fu ZW(2018)On the green function and poisson integrals of the Dunkl Laplacian Potential Anal. 48 337-360
  • [8] Grafakos L(2019)Lp-bounded Dunkl-type generalized translation operator and its applications Constr. Appr. 49 555-605
  • [9] Lu SZ(1928)Some properties of fractional integrals, I Math. Zeit. 27 565-606
  • [10] Zhao FY(2009)Riesz potentials fractional maximal function for the Dunkl transform J. Lie Theory 4 725-734
12345