Related papers: Transferring spherical multipliers on compact symm…

We develop a new approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the…

A compact semisimple Lie algebra $\mathfrak{g}$ induces a Poisson structure $\pi$ on the unit sphere $S$ in $\mathfrak{g}^*$. We compute the moduli space of Poisson structures on $S$ around $\pi$. This is the first explicit computation of a…

In this note it is shown that the class of all multipliers from the $d$-parameter Hardy space $H^1_{\mathrm{prod}} (\mathbb{T}^d)$ to $L^2 (\mathbb{T}^d)$ is properly contained in the class of all multipliers from $L \log^{d/2} L…

We give a new proof of the fact that Milnor-Witt K-theory has geometric transfers. The proof yields to a simplification of Morel's conjecture about transfers on contracted homotopy sheaves.

Let U/K represent a connected, compact symmetric space, where theta is an involution of U that fixes K, phi: U/K to U is the geodesic Cartan embedding, and G is the complexification of U. We investigate the intersection of phi(U/K) with the…

In this paper, we extend a spherical variant of the Kowalski-S\{l}odkowski theorem due to Li, Peralta, Wang and Wang. As a corollary, we prove that every 2-local map in the set of all surjective isometries (without assuming linearity) on a…

The aim of this exposition is to explain basic ideas behind the concept of diffusive wavelets on spheres in the language of representation theory of Lie groups and within the framework of the group Fourier transform given by Peter-Weyl…

Let us consider the symmetric square transfer of the automorphic representation $\pi$ associated to a modular form $f \in S_k(N,\epsilon)$. In this article, we study the variation of the epsilon factor of ${\mathrm{sym}}^2(\pi)$ under…

This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler's identity, and Dedekind zeta functions of quadratic imaginary…

For a Gelfand pair $(G,K)$ with $G$ a Lie group of polynomial growth and $K$ a compact subgroup, the "Schwartz correspondence" states that the spherical transform maps the bi-$K$-invariant Schwartz space ${\mathcal S}(K\backslash G/K)$…

We prove the first theorem on projections on general noncommutative $\mathrm{L}^p$-spaces associated with non-type I von Neumann algebras where $1 \leqslant p < \infty$. This is the first progress on this topic since the seminal work of…

This paper focuses on representations of contractively embedded invariant subspaces in several variables. We present a version of the de Branges theorem for $n$-tuples of multiplication operators by the coordinate functions on analytic…

We study the operators T on the weighted space L^p commuting either with the right translations St or left translations P^+S_{-t} and we establish the existence of a symbol of T. We characterize completely the spectrum of St. We obtain a…

In this paper we have characterized the space of summability kernels for the case p=1 and p=2. For other values of p we give a necessary condition for a function $\Lambda$ to be a summability kernel. For the case p=1, we have studied the…

In this paper we obtain new transference theorems improving some classical theorems which belong to Kurt Mahler. We formulate those theorems in terms of consecutive minima of pseudo-compound parallelepipeds.

We give an elementary proof of a compact embedding theorem in abstract Sobolev spaces. The result is first presented in a general context and later specialized to the case of degenerate Sobolev spaces defined with respect to nonnegative…

In this paper we discuss dilaton shifts (Euler counterterms) arising in decomposition of two-dimensional quantum field theories with higher-form symmetries. These take a universal form, reflecting underlying (noninvertible, quantum)…

We establish precise regularity conditions for $L_p$-boundedness of Fourier multipliers in the group algebra of $SL_n(\mathbf{R})$. Our main result is inspired by H\"ormander-Mikhlin criterion from classical harmonic analysis, although it…

The paper studies the deformation theory of a holomorphic surjective map from a normal compact complex space to a compact Kaehler manifold and describes the component of the space of holomorphic maps, generalizing results in the projective…

By means of appropriate sparse bounds, we deduce compactness on weighted $L^p(w)$ spaces, $1<p<\infty$, for all Calder\'on-Zygmund operators having compact extensions on $L^2(\mathbb{R}^n)$. Similar methods lead to new results on…