Maximal functions along twisted surfaces on product domains

Ahmad Al-Salman

doi:10.4134/BKMS.b200780

Maximal functions along twisted surfaces on product domains

Ahmad Al-Salman^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we introduce a class of maximal functions along twisted surfaces in Rⁿ ×R^m of the form {(φ(|v|)u, ϕ(|u|)v): (u, v) ∈ Rⁿ ×R^m }. We prove L^p bounds when the kernels lie in the space L^q (Sⁿ⁻¹ ×S^m−1). As a consequence, we establish the L^p boundedness for such class of operators provided that the kernels are in L log L(Sⁿ⁻¹ ×S^m−1) or in the Block spaces Bq^0,0 (Sⁿ⁻¹ ×S^m−1) (q > 1).

Original language	English
Pages (from-to)	1003-1019
Number of pages	17
Journal	Bulletin of the Korean Mathematical Society
Volume	58
Issue number	4
DOIs	https://doi.org/10.4134/BKMS.b200780
Publication status	Published - 2021
Externally published	Yes

Keywords

Block spaces
Maximal functions
Product domains
Singular integrals
Twisted surfaces

ASJC Scopus subject areas

Mathematics(all)

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10.4134/BKMS.b200780

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abstract = "In this paper, we introduce a class of maximal functions along twisted surfaces in Rn ×Rm of the form {(φ(|v|)u, ϕ(|u|)v): (u, v) ∈ Rn ×Rm }. We prove Lp bounds when the kernels lie in the space Lq (Sn−1 ×Sm−1). As a consequence, we establish the Lp boundedness for such class of operators provided that the kernels are in L log L(Sn−1 ×Sm−1) or in the Block spaces Bq0,0 (Sn−1 ×Sm−1) (q > 1).",

keywords = "Block spaces, Maximal functions, Product domains, Singular integrals, Twisted surfaces",

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note = "Publisher Copyright: {\textcopyright} 2021 Korean Mathematial Soiety.",

year = "2021",

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AB - In this paper, we introduce a class of maximal functions along twisted surfaces in Rn ×Rm of the form {(φ(|v|)u, ϕ(|u|)v): (u, v) ∈ Rn ×Rm }. We prove Lp bounds when the kernels lie in the space Lq (Sn−1 ×Sm−1). As a consequence, we establish the Lp boundedness for such class of operators provided that the kernels are in L log L(Sn−1 ×Sm−1) or in the Block spaces Bq0,0 (Sn−1 ×Sm−1) (q > 1).

KW - Block spaces

KW - Maximal functions

KW - Product domains

KW - Singular integrals

KW - Twisted surfaces

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JF - Bulletin of the Korean Mathematical Society

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Maximal functions along twisted surfaces on product domains

Abstract

Keywords

ASJC Scopus subject areas

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