Some Lp inequalities for the family of B-operators

Ahmad, Irshad and Liman, A. and Shah, W. M. (2014) Some Lp inequalities for the family of B-operators. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 30 (1). pp. 79-89. ISSN 0866-0174

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Abstract

Let Pn be the class of polynomials of degree at most n and Bn be a class of operators that map Pn into itself. For every P ∈ Pn and B ∈ Bn, we investigate on |z| = 1, the dependence of ||B[P(R ·)] − B[P(r ·)]||q on ||P||q, for every R > r ≥ 1 and q ≥ 1.

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