A Note on Vector-Valued Hardy and Paley Inequalities
نویسندگان
چکیده
منابع مشابه
Vector–valued Hardy Inequalities and B–convexity
Inequalities of the form ∑∞ k=0 |f̂(mk)| k+1 ≤ C ‖f‖1 for all f ∈ H1, where {mk} are special subsequences of natural numbers, are investigated in the vector-valued setting. It is proved that Hardy’s inequality and the generalized Hardy inequality are equivalent for vector valued Hardy spaces defined in terms of atoms and that they actually characterize B-convexity. It is also shown that for 1 < ...
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Let 2 ≤ p < ∞ and let X be a complex Banach space. It is shown that X is p-uniformly PL-convex if and only if there exists λ > 0 such that ‖f‖Hp(X) ≥ ( ‖f(0)‖p + λ ∫ D (1− |z|2)p−1‖f ′(z)‖pdA(z) )1/p , for all f ∈ Hp(X). Applications to embeddings between vector-valued BMOA spaces defined via Poisson integral or Carleson measures are provided. AMS Subject Class. 46B20,46L52
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1992
ISSN: 0002-9939
DOI: 10.2307/2159228