Anisotropic spaces Lp,ga of parabolic Bessel potentials, associated with the singular heat operator I-Dg+ \frac{\partial}{\partial t}, where Dg = \sum\limitsk=1n \frac{\partial 2}{\partial xk2} + \frac{2g }{xn}. \frac{\partial}{\partial xn}, are introduced, and making use of special wavelet-type transform, a characterization of these spaces is obtained.
📌 3 Key Takeaways
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Objective & Hypothesis:Anisotropic spaces Lp,ga of parabolic Bessel potentials, associated with the singular heat operator I-Dg+ \frac{\partial}{\partial t}, where Dg = \sum\limitsk=1n \frac{\partial 2}{\partial xk2} + \frac{2g }{xn}. \frac{\partial}{\partial xn}, are introduced, and making use of special wavelet-type transform, a characterization of these spaces is obtained.
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Key Findings & Data:Anisotropic spaces Lp,ga of parabolic Bessel potentials, associated with the singular heat operator I-Dg+ \frac{\partial}{\partial t}, where Dg = \sum\limitsk=1n \frac{\partial 2}{\partial xk2} + \frac{2g }{xn}. \frac{\partial}{\partial xn}, are introduced, and making use of special wavelet-type transform, a characterization of these spaces is obtained.
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Conclusion & Impact:Anisotropic spaces Lp,ga of parabolic Bessel potentials, associated with the singular heat operator I-Dg+ \frac{\partial}{\partial t}, where Dg = \sum\limitsk=1n \frac{\partial 2}{\partial xk2} + \frac{2g }{xn}. \frac{\partial}{\partial xn}, are introduced, and making use of special wavelet-type transform, a characterization of these spaces is obtained.
Anisotropic spaces Lp,ga of parabolic Bessel potentials, associated with the singular heat operator I-Dg+ \frac{\partial}{\partial t}, where Dg = \sum\limitsk=1n \frac{\partial 2}{\partial xk2} + \frac{2g }{xn}. \frac{\partial}{\partial xn}, are introduced, and making use of special wavelet-type transform, a characterization of these spaces is obtained.
Özet
Anisotropic spaces Lp,ga of parabolic Bessel potentials, associated with the singular heat operator I-Dg+ \frac{\partial}{\partial t}, where Dg = \sum\limitsk=1n \frac{\partial 2}{\partial xk2} + \frac{2g }{xn}. \frac{\partial}{\partial xn}, are introduced, and making use of special wavelet-type transform, a characterization of these spaces is obtained.
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Sinem SEZER, Ilham A. ALIEV Akdeniz University, Department of Mathematics, Antalya-TURKEY e-mail: [email protected] e-mail: [email protected]