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Letter to the Editor. Remarks on Some Inequalities for Polynomials

Hachani, M. A. (2013)

Mathematica Balkanica New Series

MSC 2010: 30A10, 30C10, 30C80, 30D15, 41A17.In the present article, I point out serious errors in a paper published in Mathematica Balkanica three years ago. These errors seem to go unnoticed because some mathematicians are applying the results stated in this paper to prove other results, which should not continue.

Libera and Hilbert matrix operator on logarithmically weighted Bergman, Bloch and Hardy-Bloch spaces

Boban Karapetrović (2018)

Czechoslovak Mathematical Journal

We show that if α > 1 , then the logarithmically weighted Bergman space A log α 2 is mapped by the Libera operator into the space A log α - 1 2 , while if α > 2 and 0 < ε α - 2 , then the Hilbert matrix operator H maps A log α 2 into A log α - 2 - ε 2 .We show that the Libera operator maps the logarithmically weighted Bloch space log α , α , into itself, while H maps log α into log α + 1 .In Pavlović’s paper (2016) it is shown that maps the logarithmically weighted Hardy-Bloch space log α 1 , α > 0 , into log α - 1 1 . We show that this result is sharp. We also show that H maps log α 1 , α 0 , into log α - 1 1 and...

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