Estimates of weighted Hardy–Littlewood averages on the p-adic vector space

In the p-adic vector space Q p n , we characterize those non-negative functions ψ defined on Z p * = { w ∈ Q p : 0 < | w | p ⩽ 1 } for which the weighted Hardy–Littlewood average U ψ : f → ∫ Z p * f ( t ⋅ ) ψ ( t ) d t is bounded on L r ( Q p n ) ( 1 ⩽ r ⩽ ∞ ), and on BMO ( Q p n ) . Also, in eac...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2006-12, Vol.324 (2), p.1470-1477
Main Authors: Rim, Kyung Soo, Lee, Jaesung
Format: Article
Language:English
Subjects:
Algebra
BMO
Exact sciences and technology
Mathematics
Number theory
p-Adic field
p-Adic vector space
Sciences and techniques of general use
Weighted Hardy–Littlewood averages
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Summary:In the p-adic vector space Q p n , we characterize those non-negative functions ψ defined on Z p * = { w ∈ Q p : 0 < | w | p ⩽ 1 } for which the weighted Hardy–Littlewood average U ψ : f → ∫ Z p * f ( t ⋅ ) ψ ( t ) d t is bounded on L r ( Q p n ) ( 1 ⩽ r ⩽ ∞ ), and on BMO ( Q p n ) . Also, in each case, we find the corresponding operator norm ‖ U ψ ‖ .
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2006.01.038