Abstract
In this paper, we introduce a class of singular Radon transforms on Rn with kernels supported in a subvariety in Rn× Rn determined by a polynomial mapping from Rn× Rn into Rn. The class of considered operators is related to the composition of homogeneous singular integral operators. We prove that the operators are bounded on Lp provided that the kernels are rough in L(log L) 2(Sn-1× Sn-1). The condition L(log L) 2(Sn-1× Sn-1) is observed to be optimal in the sense that the power 2 can not be replaced by a smaller number.
Original language | English |
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Article number | 48 |
Journal | Banach Journal of Mathematical Analysis |
Volume | 16 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jul 1 2022 |
Keywords
- Fourier transform
- L estimates
- Maximal functions
- Rough kernels
- Singular Radon transforms
- Singular integral operators
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory