Convergence of Convolution Operators and Weighted Averages in L(P) Spaces

It is well known that it is possible to have pointwise convergence in some Lp spaces and not in others along the Individual Ergodic Theorem. We show that the same behavior is possible for perturbed moving averages and convolution operators induced by approximate identities. Furthermore, we study weighted versions of moving averages and differentiation operators. We address the question of optimality for the classes of weights used to assure that these operators satisfy weak type inequalities. We examine similarities and differences in the behavior of these two classes of operators with respect to existence of optimal weights.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Avramidou, Parthena

Contributors dc:contributor

• Rosenblatt, Joseph

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3101795

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86817