On increasing separated sequences

On Separated Carleson Sequences in the Unit Disc

The interpolating sequences S for H∞(D), the bounded holomorphic functions in the unit disc D of the complex plane C, were characterized by L. Carleson using metric conditions on S. Alternatively, to characterize interpolating sequences we can use the existence in H∞(D) of an infinity of functions {ρa}a∈S , uniformly bounded in D, the function ρa being 1 at the point a ∈ S and 0 at any b ∈ S \ ...

A General Note on Increasing Sequences

In the present paper, a general theorem on | N̄ , pn |k summability factors of infinite series has been proved under more weaker conditions. Also we have obtained a new result concerning the | C, 1 |k summability factors.

On Almost Increasing Sequences and Its Applications

We prove a general theorem on |N̄,pn;δ|k summability factors, which generalizes a theorem of Bor (1994) on |N̄,pn|k summability factors, under weaker conditions by using an almost increasing sequence. 2000 Mathematics Subject Classification. Primary 40D15, 40F05, 40G99.

On an Application of Almost Increasing Sequences

Using an almost increasing sequence, a result of Mazhar (1977) on |C,1|k summability factors has been generalized for |C,α;β|k and |N̄,pn;β|k summability factors under weaker conditions. 2000 Mathematics Subject Classification. 40D15, 40F05, 40G05.

Quasi β-power increasing sequences