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Weighted \(L^p\) estimates for powers of selfadjoint operators. (English) Zbl 1245.42010

For bounded functions of a selfadjoint operator satisfying a pointwise Gaussian estimate for its heat kernel it is proved \(L^{p}(\omega)\) \((p>1)\) estimates for weights \(\omega\) from Muckenhoupt class \(A_p\). As an application, weighted estimates for fractional powers of an electromagnetic Schrödinger operator with singular coefficients are obtained.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
35Q55 NLS equations (nonlinear Schrödinger equations)
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