$L^p$ regularity for Kohn’s operator

Lp REGULARITY FOR CONVOLUTION OPERATOR EQUATIONS IN BANACH SPACES

Abstract. Here we utilize operator–valued Lq → Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integrodifferential equations in R. 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 ...

Maximal Lp-Regularity for Stochastic Evolution Equations

We prove maximal L-regularity for the stochastic evolution equation

On Boundedness of Weighted Hardy Operator in Lp() and Regularity Condition

Lp-continuity for Calderón–Zygmund operator

Abstract. Given a Calderón–Zygmund (C–Z for short) operator T , which satisfies Hörmander condition, we prove that: if T maps all the characteristic atoms to W L1, then T is continuous from Lp to Lp(1 < p < ∞). So the study of strong continuity on arbitrary function in Lp has been changed into the study of weak continuity on characteristic functions.

Maximal regularity for evolution equations in weighted Lp - spaces

LetX 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 anH∞-calculus in weigh...