Multilinear embedding theorem for fractional sparse operators

TL;DR

This paper establishes conditions under which multilinear embedding theorems apply to fractional sparse operators and Schrödinger operators, including power weights and Morrey-type conditions.

Contribution

It provides new sufficient conditions for multilinear embeddings and bounds for fractional sparse and Schrödinger operators, expanding theoretical understanding.

Findings

Established multilinear embedding theorem for fractional sparse operators.

Verified conditions for power weights in the theorem.

Provided Morrey-type conditions for Schrödinger operator bounds.

Abstract

We show some simple sufficient conditions for which the multilinear embedding theorem holds for fractional sparse operators. By verifying these conditions, we establish the theorem for power weights. We also provide Morrey-type sufficient conditions for which the $L^p \to L^q$, $1<p,q<\infty$, infinitesimal relative bounds hold for Schr\"{o}dinger operators of the form $(-\Delta)^{\alpha/2}+v$.