On the composition for rough singular integral operators

Abstract

In this paper, we investigate the behavior of the bounds of the composition for rough singular integral operators on the weighted space. More precisely, we obtain the quantitative weighted bounds of the composite operator for two singular integral operators with rough homogeneous kernels on $L^p({\mathbb{R}}^d,w)$, $p\in (1,\infty )$, which is smaller than the product of the quantitative weighted bounds for these two rough singular integral operators. Moreover, at the endpoint $p=1$, the $L\log L$ weighted weak type bound is also obtained, which has interests of its own in the theory of rough singular integral even in the unweighted case.

22 pages, J. Geom. Anal., to appear

References in corpus (7)

• $L^p$ bounds for singular integrals and maximal singular integrals with rough kernels
• A sparse domination principle for rough singular integrals
• Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals
• Estimates for compositions of maximal operators with singular integrals
• Sparse bounds for maximal rough singular integrals via the Fourier transform
• Sparse Bounds for Maximally Truncated Oscillatory Singular Integrals
• Weighted weak type endpoint estimates for the composition of Calderon-Zygmund operators