Quasi Grand Lebesgue Spaces

TL;DR

This paper introduces a new class of quasi-Banach spaces extending Grand Lebesgue Spaces for small parameters, exploring their properties such as completeness, duality, and operator estimates.

Contribution

It presents the first study of quasi-Green Lebesgue Spaces, detailing their fundamental properties and extending classical analysis tools to this new setting.

Findings

Spaces are complete and have well-defined duals.

Operator estimates are established within these spaces.

Key inequalities and indices are characterized.

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.