Premium
A SPLITTING PROCEDURE FOR BELLMAN FUNCTIONS AND THE ACTION OF DYADIC MAXIMAL OPERATORS ON L p
Author(s) -
Osękowski Adam
Publication year - 2015
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579314000266
Subject(s) - mathematics , action (physics) , operator (biology) , simple (philosophy) , function (biology) , maximal operator , argument (complex analysis) , pure mathematics , algebra over a field , mathematical analysis , bounded function , biochemistry , chemistry , physics , philosophy , epistemology , repressor , quantum mechanics , evolutionary biology , biology , transcription factor , gene
The purpose of the paper is to introduce a novel “splitting” procedure which can be helpful in the derivation of explicit formulas for various Bellman functions. As an illustration, we study the action of the dyadic maximal operator on L p . The associated Bellman function B p , introduced by Nazarov and Treil, was found explicitly by Melas with the use of combinatorial properties of the maximal operator, and was later rediscovered by Slavin, Stokolos and Vasyunin with the use of the corresponding Monge–Ampère partial differential equation. Our new argument enables an alternative simple derivation of B p .