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Hardy spaces for Bessel–Schrödinger operators
Author(s) -
Kania Edyta,
Preisner Marcin
Publication year - 2018
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.201600286
Subject(s) - bessel function , mathematics , operator (biology) , hardy space , space (punctuation) , function space , characterization (materials science) , pure mathematics , schrödinger's cat , type (biology) , function (biology) , mathematical analysis , physics , ecology , biochemistry , chemistry , linguistics , philosophy , repressor , evolutionary biology , biology , transcription factor , optics , gene
Consider the Bessel operator with a potential onL 2 ( ( 0 , ∞ ) , x αd x ) , namely L f ( x ) = − f ′ ′( x ) − α x f ′ ( x ) + V ( x ) f ( x ) . We assume that α > 0 and V ∈ L l o c 1 ( ( 0 , ∞ ) , x αd x )is a nonnegative function. By definition, a function f ∈ L 1 ( ( 0 , ∞ ) , x αd x )belongs to the Hardy spaceH 1 ( L )ifsup t > 0e − t L f ∈ L 1 ( ( 0 , ∞ ) , x αd x ) . Under certain assumptions on V we characterize the spaceH 1 ( L )in terms of atomic decompositions of local type. In the second part we prove that this characterization can be applied to L for α ∈ ( 0 , 1 ) with no additional assumptions on the potential V .