Maximal regularity and hardy spaces
Copyright policy )Maximal regularity and hardy spaces
In this work, we consider the Cauchy problem for $u' - Au = f$ with $A$ the Laplacian operator on some Riemannian manifolds or a sublapacian on some Lie groups or some second order elliptic operators on a domain. We show the boundedness of the operator of maximal regularity $f\mapsto Au$ and its adjoint on appropriate Hardy spaces which we define and study for this purpose. As a consequence we reobtain the maximal $L^q$ regularity on $L^p$ spaces for $p,q$ between 1 and $\infty$.
27 pages
- University of Paris-Saclay France
- Hebei University China (People's Republic of)
- School of Mathematical Sciences
- BEIJING NORMAL UNIVERSITY China (People's Republic of)
- Beijing Normal University China (People's Republic of)
Abstract parabolic equations, One-parameter semigroups and linear evolution equations, Hardy spaces, Singular and oscillatory integrals (Calderón-Zygmund, etc.), maximal regularity, Heat and other parabolic equation methods for PDEs on manifolds, \(H^p\)-spaces, Functional Analysis (math.FA), Mathematics - Functional Analysis, Linear differential equations in abstract spaces, Mathematics - Analysis of PDEs, Laplace-Beltrami operator, Mathematics - Classical Analysis and ODEs, heat kernel, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Boundary value problems on manifolds, 34G10, 35K90, 42B30, 42B20, 47D06, atomic decomposition, Analysis of PDEs (math.AP)
Abstract parabolic equations, One-parameter semigroups and linear evolution equations, Hardy spaces, Singular and oscillatory integrals (Calderón-Zygmund, etc.), maximal regularity, Heat and other parabolic equation methods for PDEs on manifolds, \(H^p\)-spaces, Functional Analysis (math.FA), Mathematics - Functional Analysis, Linear differential equations in abstract spaces, Mathematics - Analysis of PDEs, Laplace-Beltrami operator, Mathematics - Classical Analysis and ODEs, heat kernel, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Boundary value problems on manifolds, 34G10, 35K90, 42B30, 42B20, 47D06, atomic decomposition, Analysis of PDEs (math.AP)
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