Lp-BOUNDEDNESS FOR THE COMMUTATORS OF ROUGH OSCILLATORY SINGULAR INTEGRALS WITH NON-CONVOLUTION PHASES

Title & Authors
Lp-BOUNDEDNESS FOR THE COMMUTATORS OF ROUGH OSCILLATORY SINGULAR INTEGRALS WITH NON-CONVOLUTION PHASES
Wu, Huoxiong;

Abstract
In this paper, the author studies the k-th commutators of oscillatory singular integral operators with a BMO function and phases more general than polynomials. For 1 < p < $\small{\infty}$, the $\small{L^p}$-boundedness of such operators are obtained provided their kernels belong to the spaces $\small{L(log+L)^{k+1}(S^{n-1})}$. The results of the corresponding maximal operators are also established.
Keywords
commutator;oscillatory singular integral;BMO($\small{\mathbb{R}^2}$);rough kernel;
Language
English
Cited by
1.
Non-standard commutators for rough oscillatory singular integrals, Analysis in Theory and Applications, 2009, 25, 3, 230
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