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Rosenblatt, Joseph Demir, Sakin 2015-09-28T15:20:25Z 2015-09-28T15:20:25Z 10000-01-01 1999 1999 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. Made available in DSpace on 2015-09-28T15:20:25Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9944830.pdf: 3298972 bytes, checksum: 6a5f5eadac8735db9d7df0628e25cc3f (MD5) Previous issue date: 1999 Embargo set by: Seth Robbins for item 88254 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 106 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999. http://hdl.handle.net/2142/86973 (MiAaPQ)AAI9944830 eng Mathematics H(p) Spaces and Inequalities in Ergodic Theory text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.