University of Illinois Urbana-Champaign

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

Avramidou, Parthena

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Description

Title
Convergence of Convolution Operators and Weighted Averages in L(P) Spaces
Author(s)
Avramidou, Parthena
Issue Date
2003
Doctoral Committee Chair(s)
Rosenblatt, Joseph
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
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.
Graduation Semester
2003
Type of Resource
text
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http://hdl.handle.net/2142/86817

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