Riesz's and Bessel's Operators in Bilateral Grand Lebesgue Spaces
E. Ostrovsky, E. Rogover, L. Sirota
TL;DR
This paper derives non-asymptotic bounds for Riesz and Bessel potential operators within Bilateral Grand Lebesgue Spaces, demonstrating the sharpness of these inequalities through specific examples.
Contribution
It introduces new non-asymptotic estimates for these operators in Bilateral Grand Lebesgue Spaces, expanding the understanding of their behavior in these function spaces.
Findings
Derived sharp non-asymptotic bounds for Riesz and Bessel operators.
Provided examples confirming the optimality of the inequalities.
Extended the analysis of potential operators to Bilateral Grand Lebesgue Spaces.
Abstract
In this paper we obtain the non - asymptotic estimations for Riesz's and Bessel's potential integral operators in the so - called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Differential Equations and Boundary Problems