Improved range in the Return Times Theorem

TL;DR

This paper extends the Return Times Theorem to pairs of functions in L^p and L^q spaces, establishing its validity under the condition 1/p + 1/q < 3/2, thus broadening its applicability.

Contribution

It proves the Return Times Theorem for L^p-L^q pairs under a new integrability condition, expanding previous known bounds.

Findings

The theorem holds for pairs with 1/p + 1/q < 3/2.

The result generalizes previous cases with stricter conditions.

Provides a new criterion for the theorem's applicability.

Abstract

We prove that the Return Times Theorem holds true for pairs of $L^p-L^q$ functions, whenever $\frac{1}{p}+\frac{1}{q}<{3/2}$.