in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

1.1. Hardy-Sobolev-Maz’ya inequalities. Hardy inequalities and Sobolev inequalities bound the size of a function, measured by a (possibly weighted) L norm, in terms of its smoothness, measured by an integral of its gradient. Maz’ya [22] proved that for functions on the half-space R+ = {x ∈ R : xN > 0}, N ≥ 3, which vanish on the boundary, the sharp version of the Hardy inequality can be combine...

We characterize when a Hankel operator and a Toeplitz operator have a compact commutator. Let dσ(w) be the normalized Lebesgue measure on the unit circle ∂D. The Hardy space H is the subspace of L(∂D, dσ), denoted by L, which is spanned by the space of analytic polynomials. So there is an orthogonal projection P from L onto the Hardy space H, the so-called Hardy projection. Let f be in L∞. The ...

The main aim of this paper is to prove that the maximal operator σ∗ of the Fejér means of the two dimensional character system of the p-series field in the Kaczmarz rearrangement is bounded from the Hardy space Hα to the space Lα for α > 1/2, provided that the supremum in the maximal operator is taken over a positive cone. We also prove that the maximal operator σ∗ 0 of Fejér means of the two d...

In this paper, the authors obtain continuity of a class linear operators on variable anisotropic Hardy--Lorentz spaces. addition, also that dual space Hardy-Lorentz spaces is BMO-type with exponents. This result still new even when exponent function $p(\cdot)$ $p$.

We study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman–Meyer–Stein tent spaces. Following recent work of Auscher–MIntosh–Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator A with certain off-diagonal bounds, such that A always has a bounded H...

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...

in this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by bota et al. [m-f. bota, a. petrusel, g.petrusel and b. samet, coupled fixed point theorems forsingle-valued operators in b-metric spaces, fixed point theoryappl. (2015) 2015:231]. also, we prove that perov-type fixed pointtheorem in ordered gen...