Estimates for generalizated oscillatory integrals with polynomial phase

TL;DR

This paper develops uniform estimates for generalized oscillatory integrals involving Mittag-Leffler functions and polynomial phases, extending classical results with new variants of key lemmas.

Contribution

It introduces a variant of Ricci-Stein Lemma and provides invariant estimates for oscillatory integrals with Mittag-Leffler functions and polynomial phases.

Findings

Derived a new variant of Ricci-Stein Lemma.

Established invariant estimates for generalized oscillatory integrals.

Extended classical oscillatory integral estimates to Mittag-Leffler functions.

Abstract

In this paper we consider the problem on uniform estimates for generalized oscillatory integrals given by Mittag- Leffler functions with the homogeneous polynomial phase. We obtain a variant of Ricci-Stein Lemma and invariant estimates for corresponding integrals.