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Title:H(p) Spaces and Inequalities in Ergodic Theory
Author(s):Demir, Sakin
Doctoral Committee Chair(s):Rosenblatt, Joseph
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Abstract:This thesis combines the theory of ergodic Hp spaces, singular integral operators and the theory of Banach space-valued operators to establish a new method to study the inequalities for the operators induced by an ergodic, measure preserving transformation. This method also indicates the close connection between the classical theory of H p spaces and ergodic Hp spaces. By means of this connection a one sided analog of a result of B. Davis for martingale square function is proven for ergodic square function, and it is shown that one can prove the same result for a large class of operators in ergodic theory by the same method. As a corollary it is shown that one can find the integrability condition for the same class of operators analog to a result of D. S. Ornstein for the ergodic maximal function. Furthermore, it is shown that one can extend the problems of classical H p spaces to the ergodic Hp spaces, and as an application of this extension a number of inequalities in ergodic theory are proven for a large class of operators. Finally, it is shown in various perspectives that one can study the vector-valued inequalities in ergodic theory as in classical harmonic analysis. To study these inequalities some methods are introduced, and by means of these methods a large class of operators in ergodic theory is discussed extensively and various types of vector-valued inequalities are proven.
Issue Date:1999
Description:106 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999.
Other Identifier(s):(MiAaPQ)AAI9944830
Date Available in IDEALS:2015-09-28
Date Deposited:1999

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