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Acta Mathematica Vietnamica

LOGARITHMIC INTEGRALS, SOBOLEV SPACES AND RADON TRANSFORM IN THE PLANE

icon-email DANG VU GIANG

Abstract

We prove that the set {φ0,φ1,φ4,,φ3k+1,} of Hermite functions is an orthogonal system in the Sobolev space H1(R)=H(1)(R). Furthermore, the logarithmic integral of a function f from the real Hardy space H1(R) is exactly the primitive function of f~ (the Hilbert transform of f). And more interesting formulas are found for Radon transform of Hermite-like functions.