We firstly describe a maximal inequality for dual Sobolev spaces W−1,p. This one corresponds to a “Sobolev version” of usual properties of the Hardy-Littlewood maximal operator in Lebesgue spaces. Even in the euclidean space, this one seems to be new and we develop arguments in the general framework of Riemannian manifold. Then we present an application to obtain interpolation results for Sobol...

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

The α-modulation spaces M p,q , introduced by Gröbner in [10] are a class of function spaces that contain Besov spaces B p,q (α = 1) and modulation spaces M s p,q (α = 0) as special cases. There are two kinds of basic coverings on Euclidean R which is very useful in the theory of function spaces and their applications, one is the uniform covering R = ⋃ k∈Zn Qk, where Qk denote the unit cube wit...

Building on the ideas in [Lab] we indicate how the concept of a composition operator may be extended to the context of Haagerup L p-spaces.

Building on the ideas in [L1] we indicate how the concept of a composition operator may be extended to the context of Haagerup L p-spaces.