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arXiv:0901.3931 [math.AP]AbstractReferencesReviewsResources

Lp regularity for convolution operator equations in Banach spaces

Rishad Shahmurov

Published 2009-01-25, updated 2009-10-14Version 2

Here we utilize operator--valued Lq-Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integro-differential equations in Rd. Moreover, we investigate separability properties of parabolic convolution operator equations that arise in heat conduction problems in materials with fading memory. Finally, we give some remarks on optimal regularity of elliptic differential equations and Cauchy problem for parabolic equations.

Comments: 16 pages
Categories: math.AP
Subjects: 45N05, 47D06, 35J70
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