Bessel位势在空间Lp(Rn)(0 < p < 1)上的作用
The Action of the Bessel Potentials on Lp(Rn)(0 < p < 1) Space
摘要:
本文对Bessel位势在线性空间L
p(R
n)(0 < p < 1)上的作用进行了研究。利用反证法证明了对任意的r > 0，任一Bessel位势都不可能是L
p(R
n)到L
r(R
n)上的有界线性算子，并得到了其他相关的结论。
Abstract:
In this paper, we concern the action of the Bessel potentials on Lp(Rn) space with (0 < p < 1). By the method of contradiction, we prove that for any r > 0, the Bessel potential cannot be a bounded linear operator from Lp(Rn) to Lr(Rn), and obtain other related results.
参考文献
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[1]
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Adams, R.A. and Fournier, J.J.F. (2003) Sobolev Spaces. 2nd Edition, Academic Press, New York.
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[2]
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Stein, E.M. (1970) Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton. [Google Scholar] [CrossRef]
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