Orlicz Algebras on Homogeneous Spaces of Compact Groups and Their Abstract Linear Representations

Let G be a compact group, H a closed subgroup of G and let m be the normalized G-invariant measure on the homogeneous space G / H obtained from Weil’s formula. In this article, for a given Young function \(\varphi \), we give a new class of Banach convolution algebras on homogeneous spaces of compact groups by introducing a convolution and an involution on the Orlicz space \(L^\varphi (G/H, m)\). Finally, a class of linear representations of this class of Banach convolution algebras is presented.     

Ramsey theory for hypergroups

Semigroup Forum - In this paper, Ramsey theory for discrete hypergroups is introduced with emphasis on polynomial hypergroups, discrete orbit hypergroups and hypergroup deformations of semigroups....     

Multipliers on Vector-valued <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-spaces for Hypergroups

In this article, we extend the well known Wendel’s theorem to the context of vector-valued L¹-spaces on hypergroups. In this regard, various cases have been studied.     

Multipliers on Vector-valued L~1-spaces for Hypergroups

In this article, we extend the well known Wendel's theorem to the context of vector-valued L~1-spaces on hypergroups. In this regard, various cases have been studied.     

Hypercyclic sequences of weighted translations on hypergroups

Semigroup Forum - Topological procedures to relate pseudoinequalities that define a pseudovariety of ordered algebras with inequalities that ultimately define it, and vice-versa, are presented.     

$$L^p$$Lp-Boundedness and $$L^p$$Lp-Nuclearity of Multilinear Pseudo-differential Operators on $${\mathbb {Z}}^n$$Zn and the Torus $${\mathbb {T}}^n$$Tn

In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on \(L^p\)-spaces. First, we prove analogues of known multilinear Fourier multipliers theorems (proved by Coifman and Meyer, Grafakos, Tomita, Torres, Kenig, Stein, Fujita, Tao, etc.) in the context of periodic and discrete multilinear pseudo-differential operators. For this, we use the periodic analysis of pseudo-differential operators developed by Ruzhansky and Turunen. Later, we investigate the s-nuclearity, \(0<s \le 1,\) of periodic and discrete pseudo-differential operators. To accomplish this, we classify those s-nuclear multilinear integral operators on arbitrary Lebesgue spaces defined on \(\sigma \)-finite measures spaces. We also study similar properties for periodic Fourier integral operators. Finally, we present some applications of our study to deduce the periodic Kato–Ponce inequality and to examine the s-nuclearity of multilinear Bessel potentials as well as the s-nuclearity of periodic Fourier integral operators admitting suitable types of singularities.