相关论文: Nuclear pseudo-differential operators in Besov spa…

In this work we give H\"older-Besov estimates for periodic Fourier multipliers. We present a class of bounded pseudo-differential operators on periodic Besov spaces with symbols of limited regularity.

In this paper, we investigate the nuclear trace of vector-valued Fourier multipliers on the torus and its applications to the index theory of periodic pseudo-differential operators. First, we characterise the nuclearity of…

In this paper we investigate the Besov spaces on compact Lie groups in a subelliptic setting, that is, associated with a family of vector fields, satisfying the H\"ormander condition, and their corresponding sub-Laplacian. Embedding…

The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. As a consequence,…

In this paper we prove the bounded approximation property for variable exponent Lebesgue spaces, study the concept of nuclearity on such spaces and apply it to trace formulae such as the Grothendieck-Lidskii formula. We apply the obtained…

In this note we present the metric approximation property for weighted mixed-norm $L_w^{(p_1,\dots ,p_n)}$ and variable exponent Lebesgue type spaces. As a consequence, this also implies the same property for modulation and Wiener-Amalgam…

Any bounded linear operator $ T $ on $ L^2(\mathbb{R}^n) $ gives rise to the operator $ S= B \circ T \circ B^\ast $ on the Fock space $ \mathcal{F}(\C^n) $ where $ B $ is the Bargmann transform. In this article we identify those $ S $ which…

The present paper, is devoted to investigation of operator--valued Fourier multiplier theorems from $B_{q_{1},r}^{s}$ to $B_{q_{2},r}^{s}$, optimal embedding of Besov spaces, the separability and positivity of differential operators. Here,…

In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on $L^p$-spaces. First, we prove…

In this paper we study pseudo-multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to the ideal of $r$-nuclear operators on Lebesgue spaces.

We consider multilinear pseudo-differential operators with symbols in the multilinear H\"ormander class $S_{0,0}$. The aim of this paper is to discuss the boundedness of these operators in the settings of Besov spaces.

We extend the Ruzhansky-Turunen theory of pseudo differential operators on compact Lie groups into a tool that can be used to investigate group-valued Markov processes in the spirit of the work in Euclidean spaces of N.Jacob and…

This article is a continuation of our work on generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. In this article, we establish the boundedness of pseudo-differential, trace, and…

We will present versions of the Rellich-Kondrachov theorem for pseudo-differential operators acting on localizable Hardy spaces. One of the techniques includes boundedness properties for pseudodifferential operators with symbols in the…

In this paper we study the Besov continuity of pseudo-differential operators on compact homogeneous manifolds $M=G/K.$ We use the global quantization of these operators in terms of the representation theory of compact homogeneous manifolds.

In this paper we provide characterizations for the nuclearity of Fourier integral operators on $\mathbb{R}^n,$ on the discrete group $\mathbb{Z}^n,$ arbitrary compact Lie groups and compact homogeneous manifolds. We also investigate the…

In this work we establish sharp boundedness results for pseudo-differential operators corresponding to $a\in\mathcal{S}_{0,0}^{m}$ on Triebel-Lizorkin spaces $F_p^{s,q}$ and Besov spaces $B_p^{s,q}$.

Given a compact (Hausdorff) group $G$ and a closed subgroup $H$ of $G,$ in this paper we present symbolic criteria for pseudo-differential operators on compact homogeneous space $G/H$ characterizing the Schatten-von Neumann classes…

In this paper we give formulae for the Dixmier trace and the noncommutative residue (also called Wodzicki's residue) of pseudo-differential operators by using the notion of global symbol. We consider both cases, compact manifolds with or…

We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates…