English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the classes  M    p   (1 <  p  < ∞) of holomorphic functions on the open unit disk      in the complex plane. These classes are in fact generalizations of the class  M  introduced by Kim (1986). The space  M    p   equipped with the topology given by the metric   ρp   defined by   ρp  ( f ,  g ) = || f  −  g ||  p   = ( ∫   0   2  π   log  p  (1 +  M ( f  −  g )(  θ  ))( d θ  /2  π  )) 1/ p  , with  f ,  g∈M    p   and  Mf (  θ  ) = sup 0 ⩽ r<1   ⁡ | f ( re    i θ   )|, becomes an  F -space. By a result of Stoll (1977), the Privalov space  N    p   (1 <  p  < ∞) with the topology given by the Stoll metric  d    p   is an  F -algebra. By using these two facts, we prove that the spaces  M    p   and  N    p   coincide and have the same topological structure. Consequently, we describe a general form of continuous linear functionals on  M    p   (with respect to the metric   ρp  ). Furthermore, we give a characterization of bounded subsets of the spaces  M    p  . Moreover, we give the examples of bounded subsets of  M    p   that are not relatively compact.

the scientific world journal/thescientificworldjournal

On<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:math>-Algebras<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mo> </mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mi mathvariant="normal">∞</mml:mi><mml:mo stretchy="…

OnF-AlgebrasMp (1<p<∞