An inequality for the Hardy-Littlewood maximal operator with respect to a product of differentiation bases
Miguel de Guzmán (1974)
Studia Mathematica
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Miguel de Guzmán (1974)
Studia Mathematica
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Baldomero Rubio (1978)
Collectanea Mathematica
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Baldomero Rubio (1976)
Studia Mathematica
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Jan-Olav Rönning, Kathryn E. Hare (1998)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
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Soulaymane Korry (2001)
Collectanea Mathematica
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Alexander Stokolos (2005)
Annales de l’institut Fourier
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We present a simple criterion to decide whether the maximal function associated with a translation invariant basis of multidimensional intervals satisfies a weak type estimate. This allows us to complete Zygmund’s program of the description of the translation invariant bases of multidimensional intervals in the particular case of products of two cubic intervals. As a conjecture, we suggest a more precise version of Zygmund’s program.
Terasawa, Yutaka (2006)
Journal of Inequalities and Applications [electronic only]
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Leonardo Colzani, Javier Pérez Lázaro (2010)
Colloquium Mathematicae
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We prove that peak shaped eigenfunctions of the one-dimensional uncentered Hardy-Littlewood maximal operator are symmetric and homogeneous. This implies that the norms of the maximal operator on L(p) spaces are not attained.
Ireneo Peral Alonso (1977)
Collectanea Mathematica
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Soulaymane Korry (2002)
Revista Matemática Complutense
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We describe a class O of nonlinear operators which are bounded on the Lizorkin-Triebel spaces F (R), for 0 < s < 1 and 1 < p, q < ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on F (R), for 0 < s < 1 and 1 < p, q < ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H (R).