Weighted Markov-Bernstein inequalities for entire functions of exponential type
2014 ◽
Vol 96
(110)
◽
pp. 181-192
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Keyword(s):
We prove weighted Markov-Bernstein inequalities of the form ???? |f?(x)|pw(x) dx ? C(? + 1)p ???? |f(x)|pw(x) dx Here w satisfies certain doubling type properties, f is an entire function of exponential type ? ?, p > 0, and C is independent of f and ?. For example, w(x) = (1 + x2)? satisfies the conditions for any ? ? R. Classical doubling inequalities of Mastroianni and Totik inspired this result.