On non-centered maximal operators related to a non-doubling and non-radial exponential measure
Journal article, 2024

We investigate mapping properties of non-centered Hardy–Littlewood maximal operators related to the exponential measure dμ(x) = exp (- | x1| - ⋯ - | xd|) dx in Rd. The mean values are taken over Euclidean balls or cubes (ℓ∞ balls) or diamonds (ℓ1 balls). Assuming that d≥ 2 , in the cases of cubes and diamonds we prove the Lp-boundedness for p> 1 and disprove the weak type (1, 1) estimate. The same is proved in the case of Euclidean balls, under the restriction d≤ 4 for the positive part.


Adam Nowak

Polish Academy of Sciences

Emanuela Sasso

University of Genoa

Peter Sjögren

Chalmers, Mathematical Sciences

University of Gothenburg

Krzysztof Stempak

University of Wrocław

Mathematische Annalen

0025-5831 (ISSN) 1432-1807 (eISSN)

Vol. 388 3 2887-2929

Subject Categories

Algebra and Logic

Probability Theory and Statistics

Mathematical Analysis



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Latest update

3/7/2024 9