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Autumn 2019 Riesz transform and fractional integral operators generated by nondegenerate elliptic differential operators
Yoshihiro Sawano, ‎Denny Ivanal Hakim, Daniel Salim
Adv. Oper. Theory 4(4): 750-766 (Autumn 2019). DOI: 10.15352/aot.1812-1443


‎‎‎The Morrey boundedness is proved for the Riesz transform and the inverse operator of the nondegenerate elliptic differential operator of divergence form generated by a vector-function in $(L^\infty)^{n^2}$‎, ‎and for the inverse operator of the Schrödinger operators whose nonnegative potentials satisfy a certain integrability condition‎. ‎In this note‎, ‎our result is not obtained directly from the estimates of integral formula‎, ‎which reflects the fact that the solution of the Kato conjecture did not use any integral expression of the operators‎. ‎One of the important tools in the proof is the decomposition of the functions in Morrey spaces based on the elliptic differential operators in question‎. ‎In some special cases where the integral kernel comes into play‎, ‎the boundedness property of the Littlewood-Paley operator was already obtained by Gong‎. ‎So‎, ‎the main novelties of this paper are the decomposition results associated with elliptic differential operators and the result in the case where the explicit formula of the integral kernel of the heat semigroup is unavailable‎.


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Yoshihiro Sawano. ‎Denny Ivanal Hakim. Daniel Salim. "Riesz transform and fractional integral operators generated by nondegenerate elliptic differential operators." Adv. Oper. Theory 4 (4) 750 - 766, Autumn 2019.


Received: 6 December 2018; Accepted: 28 February 2019; Published: Autumn 2019
First available in Project Euclid: 15 May 2019

zbMATH: 07064103
MathSciNet: MR3949973
Digital Object Identifier: 10.15352/aot.1812-1443

Primary: 42B35
Secondary: 35J15, 47B44, 47F05

Rights: Copyright © 2019 Tusi Mathematical Research Group


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Vol.4 • No. 4 • Autumn 2019
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