Abstract:
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We prove that for d = 2, the asymptotic order of the usual Nikolskii inequality on Sd (also known as the reverse Hölder inequality) can be significantly improved in many cases, for lacunary spherical polynomials of the form f = Σm j=0 fnj with fnj being a spherical harmonic of degree nj and nj+1 - nj ≥ 3. As is well known, for d = 1, the Nikolskii inequality for trigonometric polynomials on the unit circle does not have such a phenomenon. © 2019 American Mathematical Society. |