In this paper we introduce a class of generalized Morrey spaces associated with the Schrödinger operator L = -+ V. Via a pointwise estimate, we obtain the boundedness of the operators V β 2 (-+ V)-β 1 and their dual operators on these Morrey spaces.
MSC: Primary 42B35; 42B20
Let T be an integral operator. In this paper, we introduce a L p -compactness criterion ofAs an application, we apply this criterion to deal with L p -compactness of commutators associated to Schrödinger operators with potentials in the reverse Hölder's class.
In this short note, by using a general three circle theorem, we show the rigidity of the sharp Bezout estimate first found by Gang Liu on nonnegatively curved Riemann surface.
In this paper, we obtain the precisely sharp criteria of blow-up and global existence for the cubic nonlinear beam equation in the H 2 energy-critical and H 2 sub-critical cases, respectively.
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