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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Parabolic function spaces with mixed norm

Author: V. R. Gopala Rao
Journal: Trans. Amer. Math. Soc. 246 (1978), 451-461
MSC: Primary 46E35
MathSciNet review: 515551
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Abstract: The spaces $ \mathcal{H}_\alpha ^p$ of parabolic Bessel potentials were introduced by B. F. Jones and R. J. Bagby. We prove a Sobolev-type imbedding theorem for $ \mathcal{H}_\alpha ^{{p_1},{p_2}}$ (multinormed versions of $ \mathcal{H}_\alpha ^p$) when $ \alpha $ is a positive integer k, $ 1 < {p_1}$, $ {p_2} < \infty $. In particular this theorem holds for $ W_{2l,l}^p$, since $ \mathcal{H}_{2l}^p \equiv W_{2l,l}^p$. We use the concepts of parabolic Riesz transforms and half-time derivatives introduced by us elsewhere.

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Keywords: Parabolic Bessel potentials, parabolic Riesz transforms, half-derivative, imbedding theorem
Article copyright: © Copyright 1978 American Mathematical Society

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