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Hardy Classes of Banach-Space-Valued Distributions

✍ Scribed by Oscar Blasco; José García-Cuerva

Publisher: John Wiley and Sons
Year: 1987
Tongue: English
Weight: 459 KB
Volume: 132
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19871320105

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that for O < p % I , the trigonometric polynomials are dense in HP,, the spare of B-valued harmonic functions with non-tangential maximal function in L,, if a.nd only if the BANACH space B has the RADOX-NIKODYX property (R.S.P.). This extends lrrioivn result,s for 1 < p -= -. We also show that EI% coincitlesivith t.he corresponding atomic Rpiwe if and only if B liav the R.K.P.

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In this paper (8, Z, p) will always denote a finite measure space and X a BA-NACH space. K ( p , 9) will denote the BANACH space of p-continuous X-valued measures G defined on L ? having relatively coinpact range, endowed with the semivariation norm (see Purpose of this note is to show that if X is