We establish L bounds for the Bourgain-Stein spherical maximal operator in the setting of compactly supported Borel measures μ, ν satisfying natural local size assumptions μ(B(x, r)) ≤ Crμ , ν(B(x, r)) ≤ Crν . Taking the supremum over all t > 0 is not in general possible for reasons that are fundamental to the fractal setting, but we are able to obtain single scale (t ∈ [1, 2]) results. The ran...

Ultrasound vibro-acoustography is a novel medical imaging modality that combines the high resolution of high-frequency ultrasound with the speckle-free images obtained using lowfrequency methods. This imaging modality relies on the nonlinear interaction of two high frequency beams at slightly different frequencies. We describe the physics of ultrasound vibroacoustography and outline a strategy ...

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.

Problems of existence of the singular spectrum on the continuous spectrum emerges in some mathematical aspects of quantum scattering theory and quantum solid physics. In the latter field, this phenomenon results from physical effects such as the Anderson transitions in dielectrics. In the study of this problem, selfadjoint Friedrichs model operators play an important part and constitute quite a...