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We represent a bilinear Calderon-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in a sparse $T(1)$-type bound, which in turn yields directly new sharp weighted bilinear estimates on Lebesgue and Sobolev spaces. Moreover, we apply the representation theorem to study fractional differentiation of bilinear operators, establishing Leibniz-type rules in weighted Sobolev spaces which are new even in the simplest case of the pointwise product.
This article develops a novel approach to the representation of singular integral operators of Calderon-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is realized as a fini
We study interior $L^p$-regularity theory, also known as Calderon-Zygmund theory, of the equation [ int_{mathbb{R}^n} int_{mathbb{R}^n} frac{K(x,y) (u(x)-u(y)), (varphi(x)-varphi(y))}{|x-y|^{n+2s}}, dx, dy = langle f, varphi rangle quad varphi in C
Given $2leq p<infty$, $sin (0, 1)$ and $tin (1, 2s)$, we establish interior $W^{t,p}$ Calderon-Zygmund estimates for solutions of nonlocal equations of the form [ int_{Omega} int_{Omega} Kleft (x,|x-y|,frac{x-y}{|x-y|}right ) frac{(u(x)-u(y))(varph
We deal with a global Calderon-Zygmund type estimate for elliptic obstacle problems of $p$-Laplacian type with measure data. For this paper, we focus on the singular case of growth exponent, i.e. $1<p le 2-frac{1}{n}$. In addition, the emphasis of th
In this paper, we determine the $L^p(mathbb{R})times L^q(mathbb{R})rightarrow L^r(mathbb{R})$ boundedness of the bilinear Hilbert transform $H_{gamma}(f,g)$ along a convex curve $gamma$ $$H_{gamma}(f,g)(x):=mathrm{p.,v.}int_{-infty}^{infty}f(x-t)g(x-