Lp regularity for convolution operator equations in Banach spaces

Details Lp regularity for convolution operator equations in Banach spaces Lp regularity for convolution operator equations in Banach spaces

2009-01-25

arxiv.org/abs/0901.3931v2

Mathematics

Analysis of PDEs

16 pages

Scientific paper

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.

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