Quasi Grand Lebesgue Spaces

Abstract

We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in particular, completeness, fundamental function, operators estimates, Boyd indices, contraction principle, tail behavior, dual space, generalized triangle and quadrilateral constants and inequalities.

References in corpus (5)

• Boundedness of Operators in Bilateral Grand Bebesgue Spaces with Exact and Weakly Exact Constant Calculation
• Relations between exponential tails, moments and moment generating functions for random variables and vectors
• A Banach rearrangement norm characterization for tail behavior of measurable functions (random variables)
• Bilateral Small Lebesgue Spaces
• A note about associate and dual spaces to the Grand Lebesgue ones