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Abstract

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 $ℂ^n$, and use this extension to study some related multiplier problems in $ℂ^n$.