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Strong Type Inequalities and an Almost‐Orthogonality Principle for Families of Maximal Operators Along Directions in R 2
Author(s) -
Alfonseca Angeles
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003915
Subject(s) - orthogonality , mathematics , partition (number theory) , type (biology) , maximal operator , operator (biology) , set (abstract data type) , inequality , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , computer science , geometry , ecology , biochemistry , chemistry , repressor , gene , transcription factor , bounded function , biology , programming language
The paper proves an almost‐orthogonality principle for maximal operators over arbitrary sets of directions in R 2 . Namely, the L p ‐bounds for an operator of this type are obtained from the corresponding L p ‐bounds of the maximal functions associated to a certain partition of the set of directions, and from the particular structure of this partition. Applications to several types of maximal operators are provided.