On Functions of Integrable Mean Oscillation
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On Functions of Integrable Mean Oscillation

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On Functions of Integrable Mean Oscillation

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dc.contributor.author Blasco de la Cruz, Óscar
dc.contributor.author Pérez, María Amparo
dc.date.accessioned 2010-05-04T07:53:48Z
dc.date.available 2010-05-04T07:53:48Z
dc.date.issued 2005
dc.identifier.uri http://hdl.handle.net/10550/2354
dc.language.iso en en
dc.relation http://revistas.ucm.es/mat/11391138/articulos/REMA0505220465A.PDF en
dc.source BLASCO, Oscar; PÉREZ, M. Amparo. On Functions of Integrable Mean Oscillation. En: Revista Matemática Complutense, 2005, vol. 18, no. 2, p. 465–477 en
dc.subject BMO; Módulos de continuidad en
dc.subject Mean oscillation; BMO; Modulus of continuity en
dc.title On Functions of Integrable Mean Oscillation en
dc.type info:eu-repo/semantics/article en
dc.type info:eu-repo/semantics/publishedVersion en
dc.subject.unesco UNESCO::MATEMÁTICAS en
dc.description.abstractenglish Given f 2 L1(T) we denote by wmo(f) the modulus of mean oscillation given by wmo(f)(t) = sup 0<|I| t 1 |I| Z I |f(ei ) − mI (f)| d 2 where I is an arc of T, |I| stands for the normalized length of I, and mI (f) = 1 |I| R I f(ei ) d 2 . Similarly we denote by who(f) the modulus of harmonic oscillation given by who(f)(t) = sup 1−t |z|<1 Z T |f(ei ) − P(f)(z)|Pz(ei ) d 2 where Pz(ei ) and P(f) stand for the Poisson kernel and the Poisson integral of f respectively. It is shown that, for each 0 < p < 1, there exists Cp > 0 such that Z 1 0 [wmo(f)(t)]p dt t Z 1 0 [who(f)(t)]p dt t Cp Z 1 0 [wmo(f)(t)]p dt t. en
dc.description.private -Oscar.Blasco@uv.es en

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