Related papers: Triebel--Lizorkin space estimates for multilinear …
In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calder\'on--Zygmund singular integral operator,…
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 $\mathbb{R}^d$.…
This paper is concerned with a boundedness of trace and extension operators for Besov spaces and Triebel-Lizorkin spaces on upper half space with variable exponents. To define trace and extension operators, we introduce a quarkonial…
We study the mapping property of the commutator of bilinear Hardy-Littlewood maximal operator in homogeneous Triebel-Lizorkin space. We also show that the commutator of bilinear Hardy-Littlewood maximal operator is a compact operator acting…
In this paper, the authors first discuss the characterization of Herz Triebel-Lizorkin spaces with variable exponent via two families of operators. By this characterization, the authors prove that the Lipschitz commutators of sublinear…
In this paper, we prove the boundedness of the multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces, then we give the boundedness and weak-type $L\log L$ estimates for the commutators of multilinear…
Let $H$ be a Schr\"odinger operator on $\R^n$. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with $H$ are well defined. We further give a…
In this work, some non smooth bilinear analogues of linear Littlewood-Paley square functions on the real line are studied. These bilinear operators are closely related to the bilinear Hilbert transforms and vector valued version of these…
In this paper, the authors establish the existence and boundedness of multilinear Littlewood--Paley operators on products of BMO spaces, including the multilinear $g$-function, multilinear Lusin's area integral and multilinear…
In this paper we introduce and investigate new 2-microlocal Besov and Triebel-Lizorkin space via the Littlewood-Paly decomposition. We establish characterizations of these function spaces by the $phi$-transform, the atomic and molecular…
We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.
Let $(M,\rho,\mu)$ be a metric measure space satisfying the doubling, reverse doubling and non-collapsing conditions, and $\mathscr{L}$ be a self-adjoint operator on $L^2 (M, d\mu)$ whose heat kernel $p_t (x,y)$ satisfy the small-time…
We introduce multilinear localization operators in terms of the short-time Fourier transform, and multilinear Weyl pseudodifferential operators. We prove that such localization operators are in fact Weyl pseudodifferential operators whose…
We extend to multilinear Hankel operators the fact that truncation of bounded Hankel operators is bounded. We prove and use a continuity property of a kind of bilinear Hilbert transforms on product of Lipschitz spaces and Hardy spaces.
Pseudo-differential operators of type 1,1 are proved continuous from the Triebel--Lizorkin space $F^d_{p,1}$ to $L_p$ for $1\le p<\infty$, when of order d, and this is the largest possible domain among the Besov and Triebel--Lizorkin…
This article deals with trace operators on anisotropic Lizorkin--Triebel spaces with mixed norms over cylindrical domains with smooth boundary. As a preparation we include a rather self-contained exposition of Lizorkin--Triebel spaces on…
The main result is that every pseudo-differential operator of type 1,1 and order $d$ is continuous from the Triebel--Lizorkin space $F^d_{p,1}$ to $L_p$, $1\le p<\infty$, and that this is optimal within the Besov and Triebel--Lizorkin…
In this paper, we discuss the boundedness of the fractional type Marcinkiewicz integral operators associated to surfaces, and extend a result given by Chen, Fan and Ying in 2002. They showed that under certain conditions the fractional type…
Continuing the study initiated in our earlier article [7], this paper aims to characterize various continuity properties of nonlinear composition operators acting on some sequence spaces, giving special attention to the space of sequences…
We study approximation of multivariate periodic functions from Besov and Triebel--Lizorkin spaces of dominating mixed smoothness by the Smolyak algorithm constructed using a special class of quasi-interpolation operators of…