Lp-Lq estimates of some convolution operators with singular measures on the Heisenberg group
Pablo Rocha, Tomas Godoy
TL;DR
This paper investigates the boundedness properties of specific convolution operators with singular measures on the Heisenberg group, focusing on their behavior between different Lebesgue spaces.
Contribution
It provides new Lp-Lq boundedness estimates for convolution operators with singular measures on the Heisenberg group, expanding understanding of their harmonic analysis properties.
Findings
Established Lp-Lq boundedness conditions for these operators.
Identified critical exponents for boundedness.
Extended classical results to the non-commutative setting of the Heisenberg group.
Abstract
We study the boundedness from Lp(Hn) into Lq(Hn) of certain convolution operators with singular measures on the Heisenberg group.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Holomorphic and Operator Theory