Some inequalities for entire functions

  • N. Sushchyk Ivan Franko National University of Lviv Lviv, Ukraine
  • Dzvenyslava Lukivska The Ivan Franko National University of Lviv

Анотація

Let Lp be the subspace of the space Lp(R) consisting of the restriction to the real axis of all entire functions of exponential type π. In this paper, for any function fLp(1p), we obtain estimates for the norm of f in terms of the sequence (f(n/2))nZ, namely
12fp,1fLp2fp,1,
where fp,1:=12(Jfp(Z)+JT1/2fp(Z)). Here J:Lpp(Z) is the linear operator given by the formula (Jf)(n):=(1)nf(n),nZ, and Tτ is the shift by τR of the function f,
(Tτf)(z):=f(z+τ),zC.

Біографії авторів

N. Sushchyk, Ivan Franko National University of Lviv Lviv, Ukraine

Ivan Franko National University of Lviv
Lviv, Ukraine

Dzvenyslava Lukivska, The Ivan Franko National University of Lviv

Ivan Franko National University of Lviv
Lviv, Ukraine

Посилання

B.Ya. Levin, Lectures on entire functions, Translations of Mathematical Monographs, V.150, AMS, Providence, RI, 1996.

I.S. Gradshteyn, I.M. Ryzhik, Table of integrals, series, and products, Academic Press, Editors: Daniel Zwillinger, Victor Moll, 2014. doi.org/10.1016/C2010-0-64839-5

Опубліковано
2024-09-15
Як цитувати
Sushchyk, N., & Lukivska, D. (2024). Some inequalities for entire functions. Математичні студії, 62(1), 109-112. https://doi.org/10.30970/ms.62.1.109-112
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