Optimal parameters related with continuity properties of the multilinear fractional integral operator between Lebesgue and Lipschitz spaces

TL;DR

This paper investigates the boundedness of multilinear fractional integral operators between weighted Lebesgue and Lipschitz spaces, characterizing optimal weight classes and parameter ranges for these mappings.

Contribution

It generalizes previous estimates to the multilinear and weighted setting, providing a complete characterization of weight classes and optimal parameter ranges.

Findings

Characterization of weight classes for boundedness

Identification of optimal parameter ranges

Examples of weights covering the optimal region

Abstract

We deal with the boundedness of the multilinear fractional integral operator $I_{\gamma,m}$ from a product of weighted Lebesgue spaces into adequate weighted Lipschitz spaces. Our results generalize some previous estimates not only for the linear case but also for the unweighted problem in the multilinear context. We characterize the classes of weights for which the problem described above holds and show the optimal range of the parameters involved. The optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region. We further exhibit examples of weights for the class which cover the mentioned area.