On Space of Parabolic Potentials Associated with the Singular Heat Operator

Authors: SİNEM SEZER, İLHAM A. ALİEV

Abstract: Anisotropic spaces L_{p,\gamma}^{\alpha} of parabolic Bessel potentials, associated with the singular heat operator I-\Delta_{\gamma}+ \frac{\partial}{\partial t}, where \Delta_{\gamma} = \sum\limits_{k=1}^n \frac{\partial ^{2}}{\partial x_{k}^{2}} + \frac{2\gamma }{x_n}. \frac{\partial}{\partial x_n}, are introduced, and making use of special wavelet-type transform, a characterization of these spaces is obtained.

Keywords: Generalized translation, Fourier-Bessel transform, parabolic potential, wavelet transform

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