Results 291 to 300 of about 103,531 (324)
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Mathematical Proceedings of the Cambridge Philosophical Society, 2003
The authors consider the inhomogeneous Cauchy problem \[ u'(t)= Au(t)+ f(t),\quad t\in [0,\tau),\quad u(0)= 0, \] where \(A\) is the generator of an analytic \(C_0\)-semigroup \(T(t)\) on a Banach space \(X\) and \(f\in L^p(0, \tau; X)\). They associate a closed operator \(A_1\) with \(A\) defined on \(\text{Rad}(X)\) and show that when \(X\) is a UMD ...
Arendt, Wolfgang, Bu, Shangquan
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The authors consider the inhomogeneous Cauchy problem \[ u'(t)= Au(t)+ f(t),\quad t\in [0,\tau),\quad u(0)= 0, \] where \(A\) is the generator of an analytic \(C_0\)-semigroup \(T(t)\) on a Banach space \(X\) and \(f\in L^p(0, \tau; X)\). They associate a closed operator \(A_1\) with \(A\) defined on \(\text{Rad}(X)\) and show that when \(X\) is a UMD ...
Arendt, Wolfgang, Bu, Shangquan
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Counterexamples on $L_p$ -maximal regularity
Mathematische Zeitschrift, 1999We establish a transference result for \(L^p\)-maximal regularity for the abstract Cauchy problem on Banach space.
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REGULARITY OF THE FRACTIONAL MAXIMAL FUNCTION
Bulletin of the London Mathematical Society, 2003The purpose of this work is to show that the fractional maximal operator has somewhat unexpected regularity properties. Our main result shows that the fractional maximal operator maps \(L^p\)-spaces boundedly into certain first-order Sobolev spaces. We also prove that the fractional maximal operator preserves first-order Sobolev spaces.
Kinnunen, Juha, Saksman, Eero
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Maximal regular subsemibands of SOP n
Semigroup Forum, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2015
In this paper, we prove maximal regularity estimates in “square function spaces” which are commonly used in harmonic analysis, spectral theory, and stochastic analysis. In particular, they lead to a new class of maximal regularity results for both deterministic and stochastic equations in L p -spaces with ...
Van Neerven, J.M.A.M. (author) +2 more
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In this paper, we prove maximal regularity estimates in “square function spaces” which are commonly used in harmonic analysis, spectral theory, and stochastic analysis. In particular, they lead to a new class of maximal regularity results for both deterministic and stochastic equations in L p -spaces with ...
Van Neerven, J.M.A.M. (author) +2 more
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Regular, Commutative, Maximal Semigroups of Quotients
Canadian Mathematical Bulletin, 1975A well-known theorem which goes back to R. E. Johnson [4], asserts that if R is a ring then Q(R), its maximal ring of quotients is regular (in the sense of v. Neumann) if and only if the singular ideal of R vanishes. In the theory of semigroups a natural question is therefore the following: Do there exist properties which characterize those semigroups ...
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Perturbation theorems for maximal \(L_p\)-regularity
2001The authors consider perturbation theorems for \(R\)-sectorial operators. Let \(A\) be an \(R\)-sectorial operator in a Banach space \(X\). Let \(B\) be a perturbation for \(A\) which is relatively small with respect to \(A\). Then \(A+B\) is also \(R\)-sectorial. This result seems to be a generalization of the Kato-Rellich Theorem and the KLMN-Theorem.
Kunstmann, Peer Christian, Weis, Lutz
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