Generalized Hardy inequalities and pseudocontinuable functions

Konstatin M. Dyakonov 24-1-412, Pr. Khudozhnikov, St. Petersburg, Russia

TBD mathscidoc:1701.332857

Arkiv for Matematik, 34, (2), 231-244, 1995.4
Given positive integers$n$_{1}<$n$_{2}<... we show that the Hardy-type inequality $$\sum\limits_{k = 1}^\infty {\frac{{\left| {\hat f(n_k )} \right|}}{k}} \leqslant const\left\| f \right\|1$$ holds true for all$f$∈$H$^{1}, provided that the$n$_{$k$}'s, satisfy an appropriate (and indispensable) regularity condition. On the other hand, we exhibit inifinite-dimensional subspaces of$H$^{1}for whose elements the above inequality is always valid, no additional hypotheses being imposed. In conclusion, we extend a result of Douglas, Shapiro and Shields on the cyclicity of lacunary series for the backward shift operator.
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  title={Generalized Hardy inequalities and pseudocontinuable functions},
  author={Konstatin M. Dyakonov},
  booktitle={Arkiv for Matematik},
Konstatin M. Dyakonov. Generalized Hardy inequalities and pseudocontinuable functions. 1995. Vol. 34. In Arkiv for Matematik. pp.231-244.
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