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Title:Convergence of Convolution Operators and Weighted Averages in L(P) Spaces
Author(s):Avramidou, Parthena
Doctoral Committee Chair(s):Rosenblatt, Joseph
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
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.
Issue Date:2003
Type:Text
Language:English
Description:100 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.
URI:http://hdl.handle.net/2142/86817
Other Identifier(s):(MiAaPQ)AAI3101795
Date Available in IDEALS:2015-09-28
Date Deposited:2003


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