Maximal functions and their applications최대 함수와 그 응용

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The purpose of this work is to study the relations between the nontangential maximal functions and some other function operators. In Chapter 1, we show that a certain tangential area integral of harmonic function on the upper half space $R^{n+1}$ of $R^n$ is dominated by the nontangential maximal function in $L^8$-mean. This may supplement the $L^p$-boundedness of the $g^*\lambda$-function and the nontangential area integal function for the limiting case. In Chapter 2, we prove that for nonnegative plurisubharmonic function on the unit ball B of $C_n$ the admissible maximal function is dominnated by the radial maximal function in $L^p$-maen. This gives another characterization of the class $M^p$ of holomorpic functions with certain growth condition and its invariance under the compomposition by automorphisms of B. As a consequence of the invariance, all onto-endomrphisms of $M^1$(n = 1) are characterized. In Charter 3, weprove that for nonnegative M-subharmonic functions on B the admissible maximal function is dominanted by the radial maximal function in $L^p$-mean. This domination on M-subharmonic functions implies that on plurisubhamonic functions but we include both proofs because they are interesting themselves.
Advisors
Kim, Hong-Ohresearcher김홍오researcher
Description
한국과학기술원 : 수학과,
Publisher
한국과학기술원
Issue Date
1992
Identifier
60456/325007 / 000855141
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학과, 1992.8, [ [iii], 55 p. ]

URI
http://hdl.handle.net/10203/41751
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=60456&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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