In this paper, a fractional order universal high gain adaptive stabilizer is proposed which guarantees the Lp stability of fractional order multiple–input and multiple–output (MIMO) systems with finite control effort. The boundedness of the control gain for the fractional order universal adaptive strategy is discussed for fractional order MIMO systems, and an upper bound of the control gain is ...

We estimate the distribution function of a Lagrange interpolation polynomial and deduce mean boundedness in Lp; p < 1: 1 The Result There is a vast literature on mean convergence of Lagrange interpolation, see [4{ 8] for recent references. In this note, we use distribution functions to investigate mean convergence. We believe the simplicity of the approach merits attention. Recall that if g : R...

We study a generalisation of operator spaces modelled on Lp spaces, instead of Hilbert spaces, using the notion of p-complete boundedness, as studied by Pisier and Le Merdy. We show that the Figà-Talamanca-Herz Algebras Ap(G) becomes quantised Banach algebras in this framework, and that the cohomological notion of amenability of these algebras corresponds to amenability of the locally compact g...

As it was shown by Shen, the Riesz transforms associated to Schrödinger operator L=−Δ+V are not bounded on Lp(Rd)-spaces for all p,1<p<∞, under only assumption that potential satisfies a reverse Hölder condition of order d/2, d≥3. Furthermore, they p in some finite interval type (1,p0), so can be expected preserve regularity spaces. In this work we search kind minimal additional conditions obta...

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In this paper we study the L-convergence of the Riesz means S R(f) for the sublaplacian on the sphere S in the complex n-dimensional space C. We show that S R(f) converges to f in L (S) when δ > δ(p) := (2n− 1)| 2 − 1 p |. The index δ(p) improves the one found by Alexopoulos and Lohoué [AL], 2n| 1 2 − 1 p |, and it coincides with the one found by Mauceri [Ma] and, with different methods, by Mül...

In this work we prove optimal W s,p-approximation estimates (with p P r1,`8s) for elliptic projectors on local polynomial spaces. The proof hinges on the classical Dupont– Scott approximation theory together with two novel abstract lemmas: An approximation result for bounded projectors, and an Lp-boundedness result for L2-orthogonal projectors on polynomial subspaces. The W s,p-approximation re...

We consider the hyperbolic Hardy class %Hp(B), 0 < p < ∞. It consists of φ holomorphic in the unit complex ball B for which |φ| < 1 and sup 0<r<1 ∫ ∂B {%(φ(rζ), 0)} dσ(ζ) < ∞, where % denotes the hyperbolic distance of the unit disc. The hyperbolic version of the Littlewood-Paley type g-function and the area function are defined in terms of the invariant gradient of B, and membership of %Hp(B) ...

We develop a very general operator-valued functional calculus for operators with an H∞−calculus.We then apply this to the joint functional calculus of two sectorial operators when one has an H∞calculus. Using this we prove theorem of Dore-Venni type on sums of sectorial operators and apply our results to the problem of Lp−maximal regularity. Our main assumption is the R-boundedness of certain s...