相关论文: Notes of Boundedness on Cauchy Integrals on Lipsch…

First we prove a Littlewood-Paley diagonalization result for bi-Lipschitz perturbations of the identity map on the real line. This result entails a number of corollaries for the Hilbert transform along lines and monomial curves in the…

We prove $L^p$ bounds for the extensions of standard multilinear Calder\'on-Zygmund operators to tuples of UMD spaces tied by a natural product structure. This can, for instance, mean the pointwise product in UMD function lattices, or the…

We prove that the Lipschitz-free space over a doubling metric space has the bounded approximation property. We also show that the Lipschitz-free spaces over $\ell_1^N$ or $\ell_1$ have monotone finite-dimensional Schauder decompositions.

Using Maz'ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in $R^n$. For $n\ge 8$, combined with a result in \cite{S2}, these estimates lead to the…

This paper combines explicit local calculations with covering arguments to prove the unboundedness above and below (in a logarithmic sense) of the Donaldson-Hitchin functionals on $\mathrm{G}_2$ 4-forms, $\widetilde{\mathrm{G}}_2$ 3-forms…

In the first part, we obtain sharp results for L^2 boundedness of strongly singular operators on the Heisenberg group. We also define the oscillating convolution operators on the Heisenberg group and study their boundedness properties. In…

We provide some necessary and sufficient conditions for a proper lower semicontinuous convex function, defined on a real Banach space, to be locally or globally Lipschitz continuous. Our criteria rely on the existence of a bounded selection…

Peral/Miyachi's celebrated theorem on fixed time $L^{p}$ estimates with loss of derivatives for the wave equation states that the operator $(I-\Delta)^{- \frac{\alpha}{2}}\exp(i \sqrt{-\Delta})$ is bounded on $L^{p}(\mathbb{R}^{d})$ if and…

It is shown that if the Fourier transform is a bounded map on a rearrangement-invariant space of functions on $\mathbb R^n$, modified by a weight, then the weight is bounded above and below and the space is equivalent to $L^2$. Also, if it…

Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure m. We prove that the set of of real valued Lipschitz function with non zero point-wise Lipschitz constant m-almost everywhere is residual,…

In this paper, we study the boundedness of a class of fractional integrals and derivatives associated with Laguerre polynomial expansions on Laguerre Lipschitz spaces. The consideration of such operators is motivated by the study of…

The main aim of this article is to establish boundedness of singular integrals with non-smooth kernels on product spaces. Let $L_1$ and $L_2$ be non-negative self-adjoint operators on $L^2(\mathbb{R}^{n_1})$ and $L^2(\mathbb{R}^{n_2})$,…

Our aim is to characterize the Lipschitz functions by variable exponent Lebesgue spaces. We give some characterizations of the boundedness of the maximal or nonlinear commutators of the Hardy-Littlewood maximal function and sharp maximal…

We study the $L^{2}$-boundedness of the $3$-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. Inspired by the notion of vertical perimeter, recently defined and studied by…

Given an open subset $\Omega$ of a Banach space and a Lipschitz function $u_0: \overline{\Omega} \to \mathbb{R},$ we study whether it is possible to approximate $u_0$ uniformly on $\Omega$ by $C^k$-smooth Lipschitz functions which coincide…

We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.

In this paper, by using the atomic decomposition theorem for weighted weak Hardy spaces, we will show the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and…

This paper is concerned with the problem of decomposing a higher order Lipschitz function on a closed Jordan curve $\Gamma$ into a sum of two polyanalytic functions in each open domain defined by $\Gamma$. Our basic tools are the Hardy…

We prove local Lipschitz regularity for bounded minimizers of functionals with nonstandard $p,q$-growth with the source term in the Lorentz space $L(N,1)$ under the restriction $q<p+1+p\,\min\left\{\frac 1N,\frac{2(p-1)}{Np-2p+2}\right\}$.…

We extend to multilinear Hankel operators the fact that truncation of bounded Hankel operators is bounded. We prove and use a continuity property of a kind of bilinear Hilbert transforms on product of Lipschitz spaces and Hardy spaces.