Regularity properties of Schrödinger operators
Copyright policy )Regularity properties of Schrödinger operators
Let L be a Schrödinger operator of the form L=-Δ+V, where the nonnegative potential V satisfies a reverse Hölder inequality. Using the method of L-harmonic extensions we study regularity estimates at the scale of adapted Hölder spaces. We give a pointwise description of L-Hölder spaces and provide some characterizations in terms of the growth of fractional derivatives of any order and Carleson measures. Applications to fractional powers of L and multipliers of Laplace transform type developed.
20 pages. To appear in Journal of Mathematical Analysis and Applications
- Autonomous University of Madrid Spain
- Wuhan University China (People's Republic of)
- University of La Rioja Spain
- Spanish National Research Council Spain
Schrödinger operator, fractional derivatives, harmonic extensions, Applied Mathematics, Fractional derivatives, regularity estimates in Hölder spaces, Regularity estimates in Hölder spaces, Functional Analysis (math.FA), Mathematics - Functional Analysis, Reverse Hölder inequality, Harmonic extensions, Mathematics - Analysis of PDEs, Schrödinger operator, Schrödinger equation, Special properties of functions of several variables, Hölder conditions, etc., Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, reverse Hölder inequality, Campanato spaces, Analysis, Analysis of PDEs (math.AP)
Schrödinger operator, fractional derivatives, harmonic extensions, Applied Mathematics, Fractional derivatives, regularity estimates in Hölder spaces, Regularity estimates in Hölder spaces, Functional Analysis (math.FA), Mathematics - Functional Analysis, Reverse Hölder inequality, Harmonic extensions, Mathematics - Analysis of PDEs, Schrödinger operator, Schrödinger equation, Special properties of functions of several variables, Hölder conditions, etc., Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, reverse Hölder inequality, Campanato spaces, Analysis, Analysis of PDEs (math.AP)
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