On Generalizations of Fatou's Theorem in Lp for Convolution Integrals with General Kernels

被引：0

作者：

Safaryan, M. H. ^{[1
,2
,3
]}

机构：

[1] Yerevan State Univ, Alek Manukyan 1, Yerevan 0049, Armenia

[2] Armenian Natl Acad Sci, Inst Math, Baghramian Ave 24-5, Yerevan 0019, Armenia

[3] KAUST, Thuwal 23955, Saudi Arabia

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2021年 / 31卷 / 04期

关键词：

Fatou theorem; Poisson kernel; Approximate identity; SQUARE-ROOT; POISSON KERNEL; MAXIMAL FUNCTIONS; CONVERGENCE;

D O I：

10.1007/s12220-020-00397-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove Fatou-type theorem on almost everywhere convergence of convolution integrals in spaces L-p (1 < p < infinity) for general kernels, forming an approximate identity. For a wide class of kernels, we show that obtained convergence regions are optimal in some sense. It is established a weak boundedness in L-p (1 = p < infinity) of the corresponding maximal operator.

引用

页码：3280 / 3299

页数：20

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