相关论文: Domains of type 1,1 operators: a case for Triebel-…

In this paper we continue our program of revisiting the new aspects about the boundedness properties of pseudo-differential operators on the torus. Here we prove $H^p$-$L^p$ and $H^p$-estimates for H\"ormander classes of pseudo-differential…

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…

The boundedness from $L^p \times L^q$ to $L^r$, $1<p,q \le \infty$, $0<1/p+1/q=1/r \le 1$, of bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^m_{\rho,\rho}$, $0 \le \rho <1$, is proved for the…

Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifold, fractals, graphs ...). Boundedness on $L^p$ for pseudodifferential operators of…

This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel--Lizorkin-type spaces. In this article, we obtain the sharp boundedness of almost diagonal operators on matrix-weighted…

We give a complete characterization of the continuity of pseudodifferential operators with symbols in modulation spaces $M^{p,q}$, acting on a given Lebesgue space $L^r$. Namely, we find the full range of triples $(p,q,r)$, for which such a…

We prove maximal regularity results in H\"older and Zygmund spaces for linear stationary and evolution equations driven by a large class of differential and pseudo-differential operators L, both in finite and in infinite dimension. The…

On a general Lie group $G$ endowed with a sub-Riemannian structure and of local dimension $d$, we characterize the pointwise multipliers of Triebel--Lizorkin spaces $F^{p,q}_{\alpha}$ for $p,q\in (1,\infty)$ and $\alpha>d/p$, and those of…

We introduce new classes of modulation spaces over phase space. By means of the Kohn-Nirenberg correspondence, these spaces induce norms on pseudo-differential operators that bound their operator norms on $L^p$-spaces, Sobolev spaces, and…

Let $s\ge 1$, $\omega ,\omega_0\in \mathscr P_{E,s}^0$, $a\in \Gamma _{s}^{(\omega_0)}$, and let $\mathscr B$ be a suitable invariant quasi-Banach function space, Then we prove that the pseudo-differential operator $\operatorname{Op} (a)$…

In this paper, we establish the global boundedness of oscillatory integral operators on Besov-Lipschitz and Triebel-Lizorkin spaces, with amplitudes in general $S^m_{\rho,\delta}(\mathbb{R}^n)$-classes and non-degenerate phase functions in…

The aim of this paper is to study $L^p$-boundedness property of the pseudo differential operator associated with a symbol, on rank one Riemannian symmetric spaces of noncompact type, where the symbol satisfies H\"ormander-type conditions…

We define the domain of a linear fractional transformation in a space of operators and show that both the affine automorphisms and the compositions of symmetries act transitively on these domains. Further, we show that Liouville's theorem…

In this paper, we obtain the continuity for some multilinear operators related to certain non-convolution operators on the Triebel--Lizorkin space. The operators include Littlewood--Paley operator and Marcinkiewicz operator.

In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space $F^s_{p,q}(\Omega)$ in terms of first-order differences in a uniform domain $\Omega$. The characterization is valid for any positive, non-integer real…

We give a necessary condition for a domain to have a bounded extension operator from $L^{1,p}(\Omega)$ to $L^{1,p}(\mathbb R^n)$ for the range $1 < p < 2$. The condition is given in terms of a power of the distance to the boundary of…

This is the last one of three successive articles by the authors on matrix-weighted Besov-type and Triebel--Lizorkin-type spaces $\dot B^{s,\tau}_{p,q}(W)$ and $\dot F^{s,\tau}_{p,q}(W)$. In this article, the authors establish the molecular…

This paper is devoted to the study of operator-valued Triebel-Lizorkin spaces. We develop some Fourier multiplier theorems for square functions as our main tool, and then study the operator-valued Triebel-Lizorkin spaces on $\mathbb{R}^d$.…

In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new…

Boundedness properties for pseudodifferential operators with symbols in the bilinear H\"ormander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces and, in some cases, end-point…