Results 21 to 30 of about 4,089 (272)

Discrete maximal regularity of time-stepping schemes for fractional evolution equations [PDF]

, 2017
In this work, we establish the maximal $\ell^p$-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order $\alpha\in(0,2)$, $\alpha\neq 1$, in time.
Jin, Bangti, Li, Buyang, Zhou, Zhi
core   +2 more sources

Periodic Lp estimates by R-boundedness: Applications to the Navier-Stokes equations

, 2022
General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw's transference principle, time-periodic $L^p$ estimates of maximal regularity type are established from $\mathscr{R}$-bounds of the family of solution operators ($\mathscr{R}$-solvers) to the corresponding resolvent problems. With this method,
Eiter, Thomas, Kyed, Mads, Shibata, Yoshihiro   +2 more
openaire   +3 more sources

Fourier multiplier theorems involving type and cotype [PDF]

, 2017
In this paper we develop the theory of Fourier multiplier operators $T_{m}:L^{p}(\mathbb{R}^{d};X)\to L^{q}(\mathbb{R}^{d};Y)$, for Banach spaces $X$ and $Y$, $1\leq p\leq q\leq \infty$ and $m:\mathbb{R}^d\to \mathcal{L}(X,Y)$ an operator-valued symbol ...
Rozendaal, Jan, Veraar, Mark
core   +3 more sources

Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments

Electronic Journal of Qualitative Theory of Differential Equations, 2010
In this article, the author studies the stability and boundedness of solutions for the non-autonomous third order differential equation with a deviating argument, $r$: \begin{equation*} \begin{array}{c} x^{\prime \prime \prime }(t)+a(t)x^{\prime \prime }(
Cemil Tunc
doaj   +1 more source

Maximal theorems and square functions for analytic operators on Lp-spaces [PDF]

, 2010
Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for any positive integer n.
Merdy, Christian Le, Xu, Quanhua
core   +1 more source

Operator-valued martingale transforms and R-boundedness

Illinois Journal of Mathematics, 2005
Let \((\Omega,\Phi,\mu)\) be a probability space with filtration \(\{\Phi_j,j= 0,1,2,\dots\}\) consisting of a nondecreasing sequence of subfields of \(\Phi\), and let \((X,\|.\|_X)\), \((Y,\|.\|_Y)\), \((Z,\|.\|_Z)\) be Banach spaces with norms \(\|.\|_X\), \(\|.\|_Y\), \(\|.\|_Z\).
Girardi, Maria, Weis, Lutz
openaire   +3 more sources

Generalized Fractional Integral Operators on Generalized Local Morrey Spaces

Journal of Function Spaces, 2015
We study the continuity properties of the generalized fractional integral operator Iρ on the generalized local Morrey spaces LMp,φ{x0} and generalized Morrey spaces Mp,φ. We find conditions on the triple (φ1,φ2,ρ) which ensure the Spanne-type boundedness
V. S. Guliyev, A. F. Ismayilova, A. Kucukaslan, A. Serbetci   +3 more
doaj   +1 more source

On operator valued sequences of multipliers and R-boundedness

Journal of Mathematical Analysis and Applications, 2007
Given Banach spaces \(X\) and \(Y\) as well as two spaces of sequences \(E(X)\) and \(F(Y)\) containing \(c_{00}(X)\) and \(c_{00}(Y)\), respectively, a sequence \((u_n) \subseteq L(X,Y)\) is called a \textit{multiplier sequence from \(E(X)\) to \(F(Y)\)} if the map \((x_i)\mapsto(u_ix_i)\) is bounded from \(E(X)\) into~\(F(Y)\).
Blasco, Oscar, Fourie, Jan, Schoeman, Ilse   +2 more
openaire   +2 more sources

Invariant measures for the linear stochastic Cauchy problem and R-boundedness of the resolvent [PDF]

Journal of Evolution Equations, 2006
We study the asymptotic behaviour of solutions of the stochastic abstract Cauchy problem $$ \left\{ {\begin{array}{*{20}l} {dU\left( t \right) = AU\left( t \right)dt + BdW_H \left( t \right),\quad t \geqslant 0,} \hfill\\ {U\left( 0 \right) = 0,} \hfill\\ \end{array}} \right. $$ where A is the generator of a C0-semigroup on a Banach space E, W
Van Neerven, J.M.A.M. (author), Weis, L. (author)   +1 more
openaire   +3 more sources

$L^p$-$L^q$ Maximal Regularity for some Operators Associated with Linearized Incompressible Fluid-Rigid Body Problems [PDF]

, 2017
We study an unbounded operator arising naturally after linearizing the system modelling the motion of a rigid body in a viscous incompressible fluid. We show that this operator is $\mathcal{R}$ sectorial in $L^q$ for every $q\in (1,\infty)$, thus it has ...
Maity, Debayan, Tucsnak, Marius
core   +2 more sources