Estimates for second-order Riesz transforms associated with magnetic Schrödinger operators on Musielak-Orlicz-Hardy spaces

Abstract

Let be a magnetic Schrödinger operator on , where and satisfies some reverse Hölder conditions. Assume that is a function such that is an Orlicz function, (the class of uniformly Muckenhoupt weights) and its uniformly critical lower type index . In this article, the authors prove that the operators , and are bounded from the Musielak-Orlicz-Hardy space associated with , , to the Musielak-Orlicz space , via establishing some estimates for heat kernels of . All these results are new even when , with , for all and .

Keywords:

• Musielak-Orlicz-Hardy space
• magnetic Schrödinger operator
• second-order Riesz transform
• heat kernel
• atom

AMS Subject Classifications:

• Primary: 42B20
• Secondary: 42B30
• 42B35
• 42B25
• 35J10
• 42B37
• 46E30

Notes

Jun Cao is supported by the Fundamental Research Funds for the Central Universities [grant number 2012YBXS16]. Der-Chen Chang is partially supported by an NSF [grant number DMS-1203845] and Hong Kong RGC competitive earmarked research [grant number #601410] and [grant number #601813]. Dachun Yang is supported by the National Natural Science Foundation of China [grant number 11171027] and [grant number 11361020], the Specialized Research Fund for the Doctoral Program of Higher Education of China [grant number 20120003110003] and the Fundamental Research Funds for Central Universities of China [grant number 2012LYB26] and [grant number 2012CXQT09].