Bernstein inequalities with nondoubling weights
2017
We answer Totik's question on weighted Bernstein's inequalities showing that $$ \|T_n'\|_{L_p(\omega)} \le C(p,\omega)\, {n}\,\|T_n\|_{L_p(\omega)},\qquad 0
all trigonometric polynomials $T_n$ and certain nondoubling weights $\omega$. Moreover, we find necessary conditions on $\omega$ for Bernstein's inequality to hold. We also prove weighted Bernstein-Markov, Remez, and Nikolskii inequalities for trigonometric and algebraic polynomials.
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