Boyd Indices in Generalized Grand Lebesgue Spaces and Applications

Abstract

We compute the Boyd indices of generalized grand Lebesgue spaces L p),δ and give some applications. Mathematics Subject Classification. 46E30, 46B70.

Bochner–Riesz operators in grand lebesgue spaces

“…The Grand Lebesgue Spaces and several generalizations of them have been widely investigated, mainly in the case of GLS on sets of finite measure, (see, e.g., [6,11,14,20,26,27,34,36], etc). They play an important role in the theory of Partial Differential Equations (PDEs) (see, e.g., [2,15,17,24], etc.…”

Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups equipped with Haar measure

“…The Grand Lebesgue Spaces have been widely investigated, see, e.g., [6, 7, 13, 19, 31, 32, 37, 38, 42] and references therein. They play an important role in the theory of partial differential equations (PDEs) (see, e.g., [1, 15, 17, 18, 22]), in interpolation theory (see, e.g., [2, 12, 14, 16]), in the theory of probability ([10, 20, 36, 43–45]), in statistics and in the theory of random fields (see, e.g., [35], [41, Chapter 5]), in functional analysis and so on.…”

Generalization and refinement of Khintchin's inequality

“…Recall briefly some used further facts from the theory of these spaces. Definition 2.1, see [24], [30], chapter 1, sections 1.1 -1.3; [1], [8], [9], [10], [11], [12], [13]. Let φ = φ(λ).…”