On Weak Lebesgue ( Marcinkiewicz ) Spaces with Variable Exponents
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Date
2023-06-10
Journal Title
Journal ISSN
Volume Title
Publisher
University of M'sila
Abstract
In this memory, we study the so-called Marcinkiewicz spaces ( weak Lebesgue spaces ) with
variable exponents which are one of the first generalizations of the Lebesgue spaces. In the
framework of Marcinkiewicz spaces we will study, among other topics, embedding results,
convergence in measure, interpolation results, and the question of normability of the space.
We also show a Fatou type lemma for Marcinkiewicz spaces as well as the completeness of the
quasi-norm. The Lyapunov inequality and the H¨older inequality are shown to hold.
Description
Keywords
Weak Lebesgue spaces,The Distribution Function,measure ,the variable exponent Lebesgue space , The norms, H¨older Inequality,Banach Function Spaces.