Bounds for Bilinear Analogues of the Spherical Averaging Operator

This thesis contains work from the author's papers Palsson and Sovine (2020); Iosevich, Palsson, and Sovine (2022); and Palsson and Sovine (2022) with coauthors Eyvindur Palsson and Alex Iosevich. These works establish new L^p-improving, quasi-Banach, and sparse bounds for several bilinear and multilinear operators that generalize the linear spherical average to the multilinear setting, and maximal variants of these operators, with an emphasis on the triangle averaging operator and the bilinear spherical averaging operator.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2022

Author dc:creator

• Sovine, Sean Russell

Chair dc:contributor.committeechair

• Palsson, Eyvindur Ari

Committee members dc:contributor.committeemember

• Sun, Wenbo
• Iosevich, Alexander
• Elgart, Alexander

• harmonic analysis
• multilinear operators
• geometric averages

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:34618

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/110073