Related papers: Restriction results for multilinear multipliers on…

We study a multilinear version of H\"ormander multiplier theorem, namely \begin{equation*} \Vert T_{\sigma}(f_1,\dots,f_n)\Vert_{L^p}\lesssim \sup_{k\in\mathbb{Z}}{\Vert…

We characterize strong type and weak type inequalities with two weights for positive operators on filtered measure spaces. These estimates are probabilistic analogues of two-weight inequalities for positive operators associated to the…

Let H be a Schrodinger operator with barrier potential on the real line. We define the Besov spaces for H by developing the associated Littlewood-Paley theory. This theory depends on the decay estimates of the spectral operator in the high…

We give characterizations of radial Fourier multipliers as acting on radial L^p-functions, 1<p<2d/(d+1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding…

We prove bounds for multilinear operators on $\R^d$ given by multipliers which are singular along a $k$ dimensional subspace. The new case of interest is when the rank $k/d$ is not an integer. Connections with the concept of {\em true…

In this paper we have studied Fourier multipliers and Littlewood-Paley square functions in the context of modulation spaces. We have also proved that any bounded linear operator from modulation space $\mathcal{M}_{p,q}(\R^n), 1\leq p,q\leq…

The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space $%H_{p}$ to the Lebesgue…

We introduce mixed Morrey spaces and show some basic properties. These properties extend the classical ones. We investigate the boundedness in these spaces of the iterated maximal operator, the fractional integtral operator and singular…

We consider quasiradial Fourier multipliers, i.e. multipliers of the form $m(a(\xi))$ for a class of distance functions $a$. We give a necessary and sufficient condition for the multiplier transformations to be bounded on $L^p$ for a…

Bilinear Fourier multipliers of the form $e^{i (|\xi| + |\eta|+ |\xi + \eta|)} \sigma (\xi, \eta)$ are considered. It is proved that if $\sigma (\xi, \eta)$ is in the H\"ormander class $S^{m}_{1,0} (\mathbb{R}^{2n})$ with $m=-(n+1)/2$ then…

In this paper, we prove Lp boundedness of maximal multipliers on stratified groups and maximal multipliers on product spaces of those groups.

We obtain an improved lower bound for the restricted reverse weak-type estimate of the Hardy-Littlewood maximal operator $M$. This result is applied to the $\lambda$-median maximal operator $m_{\lambda}$ acting on a Banach function space…

We describe a simple but surprisingly effective technique of obtaining spectral multiplier results for abstract operators which satisfy the finite propagation speed property for the corresponding wave equation propagator. We show that, in…

We consider degenerate differential operators $A = \displaystyle{\sum_{k,j=1}^d \partial_k (a_{kj} \partial_j)}$ on $L^2(\mathbb{R}^d)$ with real symmetric bounded measurable coefficients. Given a function $\chi \in…

Let $(X,d,\mu)$ is a space of homogeneous type, we establish a new class of fractional-type variable weights $A_{p(\cdot), q(\cdot)}(X)$. Then, we get the new weighted strong-type and weak-type characterizations for fractional maximal…

Using the standard square--function method (based on the Poisson semigroup), multiplier conditions of H\"ormander type are derived for Laguerre expansions in $L^p$--spaces with power weights in the $A_p$-range; this result can be…

We show that the Hardy-Littlewood maximal operator is bounded on a reflexive variable Lebesgue space $L^{p(\cdot)}$ over a space of homogeneous type $(X,d,\mu)$ if and only if it is bounded on its dual space $L^{p'(\cdot)}$, where…

We prove an upper bound on the sum of the distances between the eigenvalues of a perturbed Schr\"odinger operator $H_0-V$ and the lowest eigenvalue of $H_0$. Our results hold for operators $H_0=-\Delta-V_0$ in one dimension with single-well…

For $ 1\le k <n$, we prove that for functions $F,G$ on $ {\Bbb R}^{n}$, any $k$-dimensional affine subspace $H \subset {\Bbb R}^{n}$, and $p,q,r \ge 2$ with $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=1$, one has the estimate $$…

We prove norm estimates for multilinear fractional integrals acting on weighted and variable Hardy spaces. In the weighted case we develop ideas we used for multilinear singular integrals [7]. For the variable exponent case, a key element…