相关论文: Tensor, Sobolev, Multiplicative and Convolution Op…
In this note we study boundedness of a large class of maximal operators in Sobolev spaces that includes the spherical maximal operator. We also study the size of the set of Lebesgue points with respect to convergence associated with such…
Under certain restrictions we describe the set of all pointwise multipliers in case of Sobolev and Besov spaces of dominating mixed smoothness. In addition we shall give necessary and sufficient conditions for the case that these spaces…
In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded…
We study in this short preprint the theory of trigonometric approximation in the so-called Banach functional rearrangement invariant Sobolev-Grand Lebesgue Spaces.
In this short article we show a particular version of the Hedberg inequality which can be used to derive, in a very simple manner, functional inequalities involving Sobolev and Besov spaces in the general setting of Lebesgue spaces of…
In this paper we obtain the non - asymptotic estimations for Riesz's and Bessel's potential integral operators in the so - called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities.
Let $G$ a locally compact abelian group with Haar measure $\mu$ and let $1<p<\infty. $ In the present paper we determine necessary and sufficient conditions on $G$ for the grand Lebesgue space $ L^{p),\theta}(G)$ to be a Banach algebra…
We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy-Littlewood maximal operator is bounded. We also study…
We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes $S^r_{p,q}B(\mathbb{R}^d)$ with respect to pointwise multiplication. In addition…
We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…
We establish convolution inequalities for Besov spaces $B_{p,q}^s$ and Triebel--Lizorkin spaces $F_{p,q}^s$. As an application, we study the mapping properties of convolution semigroups, considered as operators on the function spaces…
In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the Dirichlet space, which is a Hilbert space. The importance of…
The question is addressed of when a Sobolev type space, built upon a general rearrangement-invariant norm, on an $n$-dimensional domain, is a Banach algebra under pointwise multiplication of functions. A sharp balance condition among the…
The reappearance of a sometimes called exotic behavior for linear and multilinear pseudodifferential operators is investigated. The phenomenon is shown to be present in a recently introduced class of bilinear pseudodifferential operators…
We study smooth function spaces of Gelfand-Shilov type, with global behavior governed through a translation-invariant Banach function space and localized via a weight function system. We clarify the roles of the translation-invariant Banach…
We prove that the Grand Lebesgue Space, builded on a unimodular locally compact topological group, forms a Banach algebra relative to the convolution.
Frame multipliers are an abstract version of Toeplitz operators in frame theory and consist of a composition of a multiplication operator with the analysis and synthesis operators. Whereas the boundedness properties of frame multipliers on…
We provide necessary and sufficient conditions for multilinear multiplier operators with symbols in $L^r$-based product-type Sobolev spaces uniformly over all annuli to be bounded from products of Hardy spaces to a Lebesgue space. We…
Motivated by a variety of representations of fractional powers of operators, we develop the theory of abstract Besov spaces $B^{ s, A }_{ q, X }$ for non-negative operators $A$ on Banach spaces $X$ with a full range of indices $s \in…
In this article we investigate the so-called Bilateral Small Lebesgue Spaces: prove that they are associated to the Grand Lebesgue spaces, calculate its fundamental functions and Boyd's indices find its dual spaces etc.