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

By K. Rim, Jaesung Lee. 2006

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Abstract 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 ‖ .

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a9aa8937bb903a208b5817d5343552669b737eba