Premium
Carleson measures and the BMO space on the p ‐adic vector space
Author(s) -
Kim YongCheol
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610806
Subject(s) - mathematics , bounded mean oscillation , prime (order theory) , dimension (graph theory) , space (punctuation) , euclidean space , bounded function , vector field , vector space , pure mathematics , field (mathematics) , mathematical analysis , combinatorics , geometry , linguistics , philosophy
Abstract For a prime number p , let Q p be the p ‐adic field and let Q pd denote a vector space over Q p which consists of all d ‐tuples of Q p . Then we study the p ‐adic version of the Calderón–Zygmund decomposition, Carleson measures on the vector space Q pd +1 and the space BMO ( Q pd ) of functions of bounded mean oscillation on Q pd . In particular, it turns out that the operator norms of various oncoming operators are independent of the dimension d and the prime number p , which is one of the big differences from that of the Euclidean case. Interestingly, the independence of the dimension d and p makes it possible to develop Harmonic Analysis on the infinite dimensional p ‐adic vector space as the importance had already been pointed out in the Euclidean case (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)