Related papers: Sharp maximal function estimates for linear and mu…
We introduce the Hardy spaces for Fourier integral operators on Riemannian manifolds with bounded geometry. We then use these spaces to obtain improved local smoothing estimates for Fourier integral operators satisfying the cinematic…
We prove quantitative matrix weighted endpoint estimates for the matrix weighted Hardy-Littlewood maximal operator, Calder\'on-Zygmund operators, and commutators of CZOs with scalar BMO functions, when the matrix weight is in the class…
In this paper we develop a Fefferman-Stein theorem, a Hardy-Littlewood theorem and sharp function estimations in weighted Sobolev spaces. We also provide uniqueness and existence results for second-order elliptic and parabolic partial…
We obtain sharp estimates for the localized distribution function of M\phi, when \phi belongs to Lp,\inf where M is the dyadic maximal operator. We obtain these estimates given the L1 and Lq norm, q < p and certain weak Lp-conditions.
In this paper, we introduce and study a class of pseudo-differential operators on the lattice $\mathbb{Z}^n$. More preciously, we consider a weighted symbol class $M_{\rho, \Lambda}^m(\mathbb{ Z}^n\times \mathbb{T}^n), m\in \mathbb{R}$…
In this paper, an approach to the one sided maximal function in the spirit of the Christ-Fefferman proof for the strong type weighted estimates of the maximal function is provided. As applications of that approach, we provide an alternative…
In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main result of the…
For a general dyadic grid, we give a Calder\'{o}n-Zygmund type decomposition, which is the principle fact about the multilinear maximal function $\mathfrak{M}$ on the upper half-spaces. Using the decomposition, we study the boundedness of…
We prove a sharp integral inequality for the dyadic maximal operator and give as an application another proof for the computation of its Bellman function of three variables.
We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on…
We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator,…
The Fefferman-Stein type inequality for strong maximal operator is verified with compositions of some maximal operators in the heigher dimensions. An elementary proof of the endpoint estimate for the strong maximal operator is also given.
We compute the Bellman function of three integral variables associated to the dyadic maximal operator on a subset of its domain. Additionally, we provide an upper bound for the whole domain of its definition.
We extend the recent boundedness result of Kurka for Hardy-Littlewood maximal function to discrete setting.
In this paper, by explicitly calculating the principal symbols of pseudodifferential operators and by applying H\"omander's spectral function theorem, we obtain the Weyl-type asymptotic formulas with sharp remainder estimates for the…
In this paper, by using the rotation method, we calculate that the sharp bound for $n$-dimensional Hardy operator $\mathcal{H}$ on mixed radial-angular spaces. Furthermore, we also obtain the sharp bound for $n$-dimensional fractional Hardy…
In this paper, we prove the boundedness of multilinear fractional integral operators from products of Hardy spaces associated with ball quasi-Banach function spaces into their corresponding ball quasi-Banach function spaces. As…
The aim of this paper is to get the product Lp-estimates, weighted estimates and two-weighted estimates for rough multilinear fractional integral operators and rough multi-sublinear fractional maximal operators, respectively. The author…
In this paper, we first obtain the operator norms of the $n$-dimensional Hardy-Littlewood-P\'{o}lya operator $\mathcal{H}$ from weighted Lebesgue spaces $L^p( \mathbb{R} ^n,| x |^{\beta} ) $ to weighted weak Lebesgue spaces…
Let $G=(V,E)$ be a finite graph and $M_G$ be the centered Hardy-Littlewood maximal operator defined there. We find the optimal value $\bf{C}_{G,p}$ such that the inequality $$\text{Var}_{p}(M_{G}f)\leq {\textbf{C}}_{G,p}\text{Var}_{p}(f)$$…