Related papers: Dilation in function spaces with general weights
We consider a dilation operator on Besov spaces $(B^s_{r,t}(K))$ over local fields and estimate an operator norm on such a field for $s > \sigma_r = \text{max}\big(\frac{1}{r} -1,~0\big)$ which depends on the constant $k$ unlike the case of…
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…
Let $X$ be a space of homogeneous type and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ satisfying Gaussian upper bounds on its heat kernels. In this paper we develop the theory of weighted Besov spaces…
In this paper, we identify the duals of Triebel-Lizorkin spaces of generalized smoothness. In some particular cases these function spaces are just weighted Triebel-Lizorkin spaces. To do these, we will be working at the level of sequence…
In this paper, we present the complex interpolation of Besov and Triebel-Lizorkin spaces with generalized smoothness. In some particular cases these function spaces are just weighted Besov and Triebel-Lizorkin spaces. An application, we…
We establish conditions on the parameters which are both necessary and sufficient in order that Besov and Triebel-Lizorkin spaces of generalized smoothness contain only regular distributions. We also connect this with the possibility of…
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of $\mathbb R^n$ via the spectral theorem for the Schr\"odinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test…
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
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…
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 establish necessary and sufficient conditions for boundedness of composition operators on the most general class of Hilbert spaces of entire Dirichlet series with real frequencies. Depending on whether or not the space contains any…
Criteria for the fulfillment of inequalities in weighted smoothness function spaces of Besov type with Riemann-Liouville operators of natural orders on the real axis and semi-axes are found. The obtained estimates are refined under…
In the present paper, we define for the Dunkl tranlation operators on the real line, the Besov-Dunkl space of functions for which the remainder in the generalized Taylor's formula has a given order. We provide characterization of these…
The aim of this paper is twofold. Firstly, we chatacterize the Besov spaces $\dot{B}_{p,q}(\mathbb{R}^{n},\{t_{k}\})$ and the Triebel-Lizorkin spaces $\dot{F}_{p,q}(\mathbb{R}^{n},\{t_{k}\})$ for $q=\infty $. Secondly, under some suitable…
Here a new condition for the geometry of Banach spaces is introduced and the operator--valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and…
In this paper we consider the generalized little Hankel and Berezin type operators on Besov spaces of holomorphic functions on polydiscs and give results about the boundedness of these operators.
Elliptic problems with additional unknown distributions in boundary conditions are investigated in Besov and Sobolev-Triebel-Lizorkin spaces of low regularity, specifically of an arbitrary negative order. We find that the problems induce…
In this paper we compute the norm of dilation operators, multidimensional Boyd`s and Shimogaki`s indices in the Bilateral Grand Lebesgue Spaces and consider some applications.
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…
In this paper we consider second order parabolic partial differential equations subject to the Dirichlet boundary condition on smooth domains. We establish weighted $L_{q}$-maximal regularity in weighted Triebel-Lizorkin spaces for such…