Abstract
Abstract This paper establishes the boundedness of the variation operators associated with Riesz transforms and commutators generated by the Riesz transforms and BMO-type functions in the Schrödinger setting on the weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.
Highlights
Given a family of bounded operators T = {Tε}ε> acting between spaces of functions, one of the most signi cative problems in harmonic analysis is the existence of limits limε→ + Tε f and limε→∞Tε f, when f belongs to a certain space of functions
This paper establishes the boundedness of the variation operators associated with Riesz transforms and commutators generated by the Riesz transforms and BMO-type functions in the Schrödinger setting on the weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class
In order to extend the boundedness of Schrödinger type operators in Lebesgue spaces, Pan and Tang [13] introduced the following weighted Morrey spaces related to the non-negative potential V, denoted by Lαp,Vλ,ω(Rn)
Summary
Abstract: This paper establishes the boundedness of the variation operators associated with Riesz transforms and commutators generated by the Riesz transforms and BMO-type functions in the Schrödinger setting on the weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class. Obtained Lp boundedness for Vq(RL,ε) and Vq(RL,ε,*) and the weighted weak type (1,1) estimation Vq(RL,ε) with the weight Aγp,θ class .
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