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BMO spaces related to Laguerre semigroups
Author(s) -
Harboure Eleonor,
Ruiz Aníbal Chicco
Publication year - 2014
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.201200227
Subject(s) - laguerre polynomials , mathematics , bounded function , semigroup , hardy space , maximal operator , pure mathematics , space (punctuation) , operator (biology) , analytic semigroup , laguerre's method , discrete mathematics , mathematical analysis , orthogonal polynomials , linguistics , philosophy , biochemistry , chemistry , repressor , transcription factor , gene , classical orthogonal polynomials
For the system of Laguerre functions { φ n α } we define a suitable BMO space from the atomic version of the Hardy spaceH φ α 1 = { f ∈ L 1 : W φ α * f ∈ L 1 }considered by Dziubański in [7][J. Dziubański, 2008], where W φ α * is the maximal operator of the heat semigroup associated to that Laguerre system. We prove boundedness of W φ α * over a weighted version of that BMO , and we extend such result to other systems of Laguerre functions, namely { L n α } and { ℓ n α } . To do that, we work with a more general family of weighted BMO ‐like spaces that includes those associated to all of the above mentioned Laguerre systems. In this setting, we prove that the local versions of the Hardy‐Littlewood and the heat‐diffusion maximal operators turn to be bounded over such family of spaces for A l o c 1 weights. This result plays a decisive role in proving the boundedness of Laguerre semigroup maximal operators.