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Volume 4, Issue 3, Article 50 |
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Convolution Inequalities and Applications
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Authors: |
Saburou Saitoh, Vu Kim Tuan, Masahiro Yamamoto, |
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Keywords:
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Convolution, Heat source, Weighted convolution inequalities, Young's inequality, Hölder's inequality, Reverse Hölder's inequality, Green's function, Stability in inverse problems, Volterra's equation, Conditional stability of Hölder type, Analytic semigroup, Interpolation inequality, Sobolev inequality. |
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Date Received:
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09/12/02 |
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Date Accepted:
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15/04/03 |
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Subject Codes: |
44A35,26D20
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Editors: |
Lars-Erik Persson, |
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Abstract: |
We introduce various convolution inequalities obtained recently and at the same time, we give new type of reverse convolution inequalities and their important applications to inverse source problems. We consider the inverse problem of determining  ,  , in the heat source of the heat equation  ,  ,  from the observation  , , at a remote point  away from the support of  . Under an a priori assumption that  changes the signs at most  -times, we give a conditional stability of Hölder type, as an example of applications.
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