Analysis Mathematica

, Volume 24, Issue 1, pp 79–89 | Cite as

BMO- andL p -conditions for power series and Dirichlet series with positive coefficients

  • V. I. Kolyada
  • L. Leindler


It is known that theL p -norms of the sums of power series can be estimated from below and above by means of their coefficients, provided these coefficients are nonnegative. In the paper we prove analogous estimates for theL p -norms of the sums of Dirichlet series. Our main result gives exact lower and upper estimates for the BMO-norm of the sums of power series and Dirichlet series, respectively, by means of their coefficients.


Power Series Hardy Space Positive Coefficient Dirichlet Series Analogous Estimate 
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BMO-иL p -условия для степенных рядов и рядов Дирихле с положительными коэффициентами


Известно, чтоL p -нормы сумм степенных рядов допускают двусторонние оценки через их коэффициенты, если эти коэффициенты положительны. В статье доказываются аналогичные оценки дляL p -норм сумм рядов Дирихле. Основным результатом статьи являются точные двусторонние оценки BMO-норм сумм степенных рядов Дирихле через их коэффициенты.


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Copyright information

© Akadémiai Kiadó 1998

Authors and Affiliations

  • V. I. Kolyada
    • 1
  • L. Leindler
    • 2
  1. 1.Odessa State UniversityOdessaUkraine
  2. 2.Bolyai InstituteUniversity of SzegedSzegedHungary

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