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Norm and Taylor coefficients estimates of holomorphic functions in balls

Jacob BurbeamDo Young Kwak — 1991

Annales Polonici Mathematici

A classical result of Hardy and Littlewood states that if f ( z ) = m = 0 a m z m is in H p , 0 < p ≤ 2, of the unit disk of ℂ, then m = 0 ( m + 1 ) p - 2 | a m | p c p f p p where c p is a positive constant depending only on p. In this paper, we provide an extension of this result to Hardy and weighted Bergman spaces in the unit ball of n , and use this extension to study some related multiplier problems in n .

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