For $p,q\in [1,\infty)$, we study the isomorphism problem for $p$- and $q$-convolution algebras associated to locally compact groups. While it is well known that not every group can be recovered from its von Neumann algebra, show this case $\mathrm{CV}_p(G)$ of $p$-convolvers $\mathrm{PM}_p(G)$ $p$-pseudomeasures, $p\neq 2$. More generally, if isometrically isomorphic $\mathrm{CV}_q(H)$, with $...

In this paper, we give the necessary and sufficient conditions for boundedness of Hardy-Ces?ro operators on some weighted function spaces such as central Morrey, local non-local Herz Morrey-Herz type with variable exponent.

The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on Rn are bounded from HK̇11 q1 × HK̇ α2,p2 q2 into HK̇ q if and only if they have vanishing moments up to a certain order dictated by the target space. Here HK̇ q are homogeneous Herz-type Hardy spaces with 1/p = 1/p1 +1/p2, 0 < pi ≤ ∞, 1/q = 1/q1 +1/q2, 1 < q1, q2 < ∞, 1 ≤ q < ∞, α = α1 + α2 a...

In this paper, we prove the boundedness of the multilinear commutator related to the singular integral operator in Morrey and Morrey-Herz spaces on homogeneous spaces. 2000 Mathematics Subject Classification: 42B20, 42B25. 1. Preliminaries Sawano and Tanka(see [13]) introduced the Morrey spaces on the non-homogeneous spaces and proved the boundedness of Hardy-Littlewood maximal operators, Calde...

The development of theoretical models and experimental methods of cell mechanics are actual task. On the bases of the shell theory we consider the elastic properties of the cells and compeer them with the experimental resuts which was received using atomic force microscopy (AFM) date. The experimental calculations were made on the bases of the Herz model. It was shown that the shell theory allo...

Luminescent quantum dots (QDs) or rods are semiconductor nano-particles that may be used for a wide array of applications such as in electro-optical devices, spectral bar coding, tagging and light filtering. In the case under investigation, the nano-particles are cadmium-selenide (CdSe), though they can be made from cadmium-sulfide, cadmium-telluride or a number of other II-VI and III-V materia...

In this paper, we establish the boundedness of commutators generated by weighted Lipschitz functions and Calderón-Zygmund singular integral operators on weighted Herz spaces.