Singular Integral Operators Supported in Higher Dimensional Surfaces

Ahmad Al-Salman

doi:10.1007/s00009-023-02476-1

Singular Integral Operators Supported in Higher Dimensional Surfaces

Ahmad Al-Salman^*

^*Corresponding author for this work

Mathematics

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

Abstract

Motivated by the composition of singular integral operators, we introduce a class of singular integral operators in the Euclidean space Rⁿ with kernels supported in surfaces in Rⁿ× Rⁿ . The surfaces are allowed to be very flat at the origin in Rⁿ× Rⁿ . The boundedness of the operators on L^p is proved under the assumption that the kernels are rough in L(log L) ²(Sⁿ^-¹× Sⁿ^-¹) .

Original language	English
Article number	275
Journal	Mediterranean Journal of Mathematics
Volume	20
Issue number	5
DOIs	https://doi.org/10.1007/s00009-023-02476-1
Publication status	Published - Jul 31 2023

Keywords

Fourier transform
L estimates
Singular integral operators
maximal functions
rough kernels
singular Radon transforms

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-023-02476-1

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abstract = "Motivated by the composition of singular integral operators, we introduce a class of singular integral operators in the Euclidean space Rn with kernels supported in surfaces in Rn× Rn . The surfaces are allowed to be very flat at the origin in Rn× Rn . The boundedness of the operators on Lp is proved under the assumption that the kernels are rough in L(log L) 2(Sn-1× Sn-1) .",

keywords = "Fourier transform, L estimates, Singular integral operators, maximal functions, rough kernels, singular Radon transforms",

author = "Ahmad Al-Salman",

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N2 - Motivated by the composition of singular integral operators, we introduce a class of singular integral operators in the Euclidean space Rn with kernels supported in surfaces in Rn× Rn . The surfaces are allowed to be very flat at the origin in Rn× Rn . The boundedness of the operators on Lp is proved under the assumption that the kernels are rough in L(log L) 2(Sn-1× Sn-1) .

AB - Motivated by the composition of singular integral operators, we introduce a class of singular integral operators in the Euclidean space Rn with kernels supported in surfaces in Rn× Rn . The surfaces are allowed to be very flat at the origin in Rn× Rn . The boundedness of the operators on Lp is proved under the assumption that the kernels are rough in L(log L) 2(Sn-1× Sn-1) .

KW - Fourier transform

KW - L estimates

KW - Singular integral operators

KW - maximal functions

KW - rough kernels

KW - singular Radon transforms

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Singular Integral Operators Supported in Higher Dimensional Surfaces

Abstract

Keywords

ASJC Scopus subject areas

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