Maximal regularity for evolution equations in weighted L p -spaces

@inproceedings{Prss2004MaximalRF,
  title={Maximal regularity for evolution equations in weighted L p -spaces},
  author={Jan Pr{\"u}ss and Gieri Simonett},
  year={2004}
}
Let X be a Banach space and let A be a closed linear operator on X. It is shown that the abstract Cauchy problem u̇(t) + Au(t) = f (t), t > 0, u(0) = 0, enjoys maximal regularity in weighted Lp-spaces with weights ω(t) = tp(1−μ), where 1/p < μ, if and only if it has the property of maximal Lp-regularity. Moreover, it is also shown that the derivation operator D = d/dt admits an H∞-calculus in weighted Lp-spaces. Introduction. Let X be a Banach space and let A be a closed linear operator on X… CONTINUE READING
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