Abstract
We investigate the boundedness and the compactness of the mean operator matrix acting on the weighted Hardy spaces.
Highlights
First in the following, we generalize the definitions coming in 1
In Theorem 2.9, we extend the method used in 20, Theorem 1.2 to show the boundedness of the mean operator matrix acting on the weighted Hardy spaces
We define an operator acting on Hp β and we will investigate its boundedness and compactness on Hp β
Summary
We generalize the definitions coming in 1. Let β {β n } be a sequence of positive numbers with β 0. Sequences f {f n }n 0 such that 1 and 1 < p < ∞. We consider the space of fp f p β fn p β n p. The notation fz f n zn n0 will be used whether or not the series converges for any value of z. These are called formal power series and the set of such series is denoted by Hp β. Recall that Hp β is a reflexive Banach space with norm · β and the dual of Hp β is Hq βp/q where 1/p 1/q 1 and βp/q {β n p/q} 2. For some other sources on this topic see 1–12
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