Related papers: Maximal multiplier on Stratified groups

The main goal of this note is to show that (not necessarily holomorphic) multipliers of a wide class of normed spaces of continuous functions over a connected Hausdorff topological space cannot attain their multiplier norms, unless they are…

Resolving the details of an object from coarse-scale measurements is a classical problem in applied mathematics. This problem is usually formulated as extrapolating the Fourier transform of the object from a bounded region to the entire…

We establish $L^{p_1}\times\cdots\times L^{p_k}\to L^r$ and $\ell^{p_1}\times\cdots\times \ell^{p_k}\to \ell^r$ type bounds for multilinear maximal operators associated to averages over isometric copies of a given non-degenerate $k$-simplex…

Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…

We find necessary and sufficient conditions for the product of two truncated Toeplitz operators on a model space to itself be a truncated Toeplitz operator, and as a result find a characterization for the maximal algebras of bounded…

We give upper bounds on limit multiplicities of certain non-tempered representations of unitary groups $U(a,b)$. These include some cohomological representations, and we give applications to the growth of cohomology of cocompact arithmetic…

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…

For a subfamily of multiplicative measures on integer partitions we give conditions for properly rescaled associated Young diagrams to converge in probability to a certain deterministic curve named the limit shape of partitions. We provide…

Moment polytopes of tensors, the study of which is deeply rooted in invariant theory, representation theory and symplectic geometry, have found relevance in numerous places, from quantum information (entanglement polytopes) and algebraic…

We establish endpoint estimates for a class of oscillating spectral multipliers on Lie groups of Heisenberg type. The analysis follows an earlier argument due to the second and fourth author but requires the detailed analysis of the wave…

In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool…

We give an explicit classification of maximal antipodal sets in any irreducible compact symmetric space except for spin groups and half spin groups, and some quotient symmetric spaces associated to them.

We study the problem of L^p-boundedness (1 < p < \infty) of operators of the form m(L_1,...,L_n) for a commuting system of self-adjoint left-invariant differential operators L_1,...,L_n on a Lie group G of polynomial growth, which generate…

In a recent work, P. Chen and E. M. Ouhabaz proved a $p$-specific $L^p$-spectral multiplier theorem for the Grushin operator acting on $\mathbb{R}^{d_1}\times\mathbb{R}^{d_2}$ which is given by \[ L =-\sum_{j=1}^{d_1} \partial_{x_j}^2 -…

We study the class $\mathcal{M}_p$ of Schur multipliers on the Schatten-von Neumann class $\mathcal{S}_p$ with $1 \leq p \leq \infty$ as well as the class of completely bounded Schur multipliers $\mathcal{M}_p^{cb}$. We first show that for…

We prove endpoint bounds for the square function associated with radial Fourier multipliers acting on $L^{p}$ radial functions. This is a consequence of endpoint bounds for a corresponding square function for Hankel multipliers. We obtain a…

We obtain bounds for the size of the Schur multiplier of finite $p$-groups and finite groups, which improve all existing bounds. Moreover, we obtain bounds for the size of the second cohomology group $H^2(G,\mathbb{Z}/p\mathbb{Z})$ of a…

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a…

This thesis is devoted to the study of multivariate (joint) spectral multipliers for systems of strongly commuting non-negative self-adjoint operators, $L=(L_1,\ldots,L_d),$ on $L^2(X,\nu),$ where $(X,\nu)$ is a measure space. By strong…