相关论文: Pointwise Multiplication by the Characteristic Fun…

Let $X$ be a space of homogeneous type and let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ which satisfies a Gaussian estimate on its heat kernel. In this paper we prove a H\"omander type spectral multiplier theorem for $L$ on…

We give characterizations of radial Fourier multipliers as acting on radial L^p-functions, 1<p<2d/(d+1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding…

We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible $\zed$-valued…

The generalization, similarly to exponential multivariate bases in the Fourier transform, of the Bessel functions to many dimensions is offered. Analogously to the Fourier transform property under the differentiation, the similar Hankel…

We review properties of Bessel potentials, that is, inverse Fourier transforms of (regularizations of) $\frac{1}{(m^2+p^2)^{\frac{\mu}{2}}}$ on a pseudoEuclidean space with signature $(q,d-q)$. We are mostly interested in the Lorentzian…

We consider multiplication properties of elements in weighted Fourier Lebesgue and modulation spaces. Especially we extend some results by Pilipovic, Teofanov and Toft (2010).

New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces.…

We prove vector-valued boundedness of (suitable) Calderon-Zygmund operators and of the (truncated) Hardy-Littlewood maximal function on a connected locally doubling metric measure space.

We prove an algebra property under pointwise multiplication for Besov spaces defined on Lie groups of polynomial growth. When the setting is restricted to the case of H-type groups, this algebra property is generalized to paraproduct…

In this paper, some properties on weighted modulation and Wiener amalgam spaces are characterized by the corresponding properties on weighted Lebesgue spaces. As applications, sharp conditions for product inequalities, convolution…

We study Besov capacities in a compact Ahlfors regular metric measure space by means of hyperbolic fillings of the space. This approach is applicable even if the space does not support any Poincar\'e inequalities. As an application of the…

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 introduce truncated Besov and Triebel--Lizorkin function spaces and investigate their main properties: embeddings, interpolation, duality, lifting, traces. These new scales allow us to improve several known results in functional analysis…

We study traces of weighted Triebel-Lizorkin spaces $F^s_{p,q}({\mathbb R}^n,w)$ on hyperplanes ${\mathbb R}^{n-k}$, where the weight is of Muckenhoupt type. We concentrate on the example weight $w_\alpha(x) = |x_n|^\alpha$ when $|x_n|\leq…

We review how some multianalytic inner functions of the Beurling type theorem are associated to row contractions following works of G.Popescu. Motivated by a result on weak Markov dilations, we define a notion of characteristic function for…

In this paper we study the multiplicative, tensor, Sobolev's and convolution inequalities in certain Banach spaces, the so-called Bide - Side Grand Lebesque Spaces, and give examples to show their sharpness.

We describe certain new spaces of coefficient multipliers of analytic Lizorkin-Triebel $F^{p,q}_{\alpha}$ type spaces in the unit polydisk with some restrictions on parameters.This extends some previously known assertions on coefficient…

We obtain an asymptotic representation formula for harmonic functions with respect to a linear anisotropic nonlocal operator. Furthermore we get a Bourgain-Brezis-Mironescu type limit formula for a related class of anisotropic nonlocal…

We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…

We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \mathbb R $ endowed with a measure which needs not to be doubling.