Related papers: Weighted norm inequalities for convolution and Rie…

We prove a T1 theorem for fractional vector Riesz transforms mapping one weighted Sobolev space to another, where the weights are doubling measures on Euclidean space. Boundedness is characterized by the classical A_2 condition and two dual…

Let $X$ be a space of homogeneous type and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ satisfying Gaussian upper bounds on its heat kernels. In this paper we develop the theory of weighted Besov spaces…

In this note we prove a multilinear version of the reverse H\"older inequality in the theory of Muckenhoupt $A_p$ weights. We give two applications of this inequality to the study of multilinear weighted norm inequalities. First, we prove a…

Considering potentials defined by Bessel kernel with Bessel convolution a Kerman-Sawyer type characterization of trace inequality is given. As an application an estimate on the least eigenvalue of Schr\"odinger-Bessel operators is derived.

Fix $d \geq 3$ and $1 < p < \infty$. Let $V : \mathbb{R}^{d} \rightarrow [0,\infty)$ belong to the reverse H\"{o}lder class $RH_{d/2}$ and consider the Schr\"{o}dinger operator $L_{V} := - \Delta + V$. In this article, we introduce classes…

We consider various versions of fractional Leibniz rules (also known as Kato-Ponce inequalities) with polynomial weights $\langle x\rangle^a = (1+|x|^2)^{a/2}$ for $a\ge 0$. We show that the weighted Kato-Ponce estimate with the…

Fourier series in orthogonal polynomials with respect to a measure $\nu$ on $[-1,1]$ are studied when $\nu$ is a linear combination of a generalized Jacobi weight and finitely many Dirac deltas in $[-1,1]$. We prove some weighted norm…

In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted…

Fix an integer $ n$ and number $d$, $ 0< d\neq n-1 \leq n$, and two weights $ w$ and $ \sigma $ on $ \mathbb R ^{n}$. We two extra conditions (1) no common point masses and (2) the two weights separately are not concentrated on a set of…

Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…

We investigate one and two weight norm inequalities for product fractional integrals. We show that in the one weight case, most of the 1 parameter theory carries over to the 2 parameter setting. However, in the two weight case, apart from…

The purpose of this article is to present one and two-weight inequalities for bilinear multiplier operators in Dunkl setting with multiple Muckenhoupt weights. In order to do so, new results regarding Littlewood-Paley type theorems and…

We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of…

In this paper we prove an optimal estimate for the norm of wavelet localization operators with Cauchy wavelet and weight functions that satisfy two constraints on different Lebesgue norms. We prove that multiple regimes arise according to…

In this paper we study the boundedness in weighted variable Lebesgue spaces of operators associated with the semigroup generated by the time-independent Schr\"odinger operator $\mathcal{L}=-\Delta+V$ in $\mathbb{R}^d$, where $d>2$ and the…

In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As…

We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue quasi-norms by Wiener amalgam ones. In these generalized Hardy spaces, we prove that some classical linear operators such as Calder\'on-Zygmund,…

In this paper, we prove the Hardy-Leray inequality and related inequalities in variable Lebesgue spaces. Our proof is based on a version of the Stein-Weiss inequality in variable Lebesgue spaces derived from two weight inequalities due to…

In this paper one-weight inequalities with general weights for Riemann-Liouville transform and $ n-$ dimensional fractional integral operator in variable exponent Lebesgue spaces defined on $\mathbb{R}^{n}$ are investigated. In particular,…

The paper concerns the magnetic Schr\"odinger operator on $R^n$. Under certain conditions, given in terms of the reverse H\"older inequality on the magnetic field and the electric potential, we prove some $L^p$ estimates on the Riesz…