Variations on the theme of Marcinkiewicz’ inequality
Copyright policy )Variations on the theme of Marcinkiewicz’ inequality
We present a new approach to the Marcinkiewicz interpolation inequality for the distribution function of the Hilbert transform, and prove an "abstract" version of this inequality. The approach uses "logarithmic determinants" and new estimates of canonical products of genus one.
32 pages
- Tel Aviv University Israel
- Bilkent University Turkey
Riesz' inequality, logarithmic determinant, Mathematics - Complex Variables, Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions, Marcinkiewicz' inequality, Hilbert transform, FOS: Mathematics, Special integral transforms (Legendre, Hilbert, etc.), Kolmogorov's weak \(L^{1}\)-type inequality, Complex Variables (math.CV), subharmonic function, 30D20, 42A50
Riesz' inequality, logarithmic determinant, Mathematics - Complex Variables, Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions, Marcinkiewicz' inequality, Hilbert transform, FOS: Mathematics, Special integral transforms (Legendre, Hilbert, etc.), Kolmogorov's weak \(L^{1}\)-type inequality, Complex Variables (math.CV), subharmonic function, 30D20, 42A50
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