On the properties of rearrangement-invariant quasi-Banach function spaces

Abstract

This paper explores some important aspects of the theory of rearrangement-invariant quasi-Banach function spaces. We focus on two main topics. Firstly, we prove an analogue of the Luxemburg representation theorem for rearrangement-invariant quasi-Banach function spaces over resonant measure spaces. Secondly, we develop the theory of fundamental functions and endpoint spaces.

References in corpus (9)

• Banach function spaces done right
• Extrapolation in general quasi-Banach function spaces
• Optimal Orlicz domains in Sobolev embeddings into Marcinkiewicz spaces
• On Bilinear Hardy Inequality and Corresponding Geometric Mean Inequality
• Reduction principle for Gaussian $K$-inequality
• Optimal Sobolev embeddings for the Ornstein-Uhlenbeck operator
• Discretization and antidiscretization of Lorentz norms with no restrictions on weights
• Optimal Gagliardo-Nirenberg interpolation inequality for rearrangement invariant spaces
• Maximal noncompactness of embeddings into Marcinkiewicz spaces

Cited by in corpus (2)

• Non-improvability of sharp endpoint estimates
• Absolute continuity of the (quasi)norm in rearrangement-invariant spaces