Hardy Classes of Banach‐Space‐Valued Distributions | Zendy

Blasco Oscar | Zendy; GarcíaCuerva José | Zendy

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Hardy Classes of Banach‐Space‐Valued Distributions

Author(s) -

Blasco Oscar,

GarcíaCuerva José

Publication year - 1987

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.19871320105

Subject(s) - mathematics , banach space , trigonometric functions , pure mathematics , space (punctuation) , property (philosophy) , eberlein–šmulian theorem , mathematical analysis , lp space , geometry , epistemology , philosophy , linguistics

It is shown that for 0< p ≥ 1, the trigonometric polynomials are dense in H B p , the space of B ‐valued harmonic functions with non‐tangential maximal function in L p , if and only if the Banach space B has the Radon‐Nikodym property (R.N.P.). This extends known results for 1 < p < ∞. We also show that H B pcoincides with the corresponding atomic space if and only if B has the R.N.P.

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