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Schauder decompositions and multiplier theorems

P. Clément, B. de Pagter, F. Sukochev, H. Witvliet (2000)

Studia Mathematica

We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for L p -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.

Second order elliptic operators with complex bounded measurable coefficients in  L p , Sobolev and Hardy spaces

Steve Hofmann, Svitlana Mayboroda, Alan McIntosh (2011)

Annales scientifiques de l'École Normale Supérieure

Let  L be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with L , such as the heat semigroup and Riesz transform, are not, in general, of Calderón-Zygmund type and exhibit behavior different from their counterparts built upon the Laplacian. The current paper aims at a thorough description of the properties of such operators in  L p , Sobolev, and some new Hardy spaces naturally associated to  L . First, we show that the...

Section spaces of real analytic vector bundles and a theorem of Grothendieck and Poly

Dietmar Vogt (2010)

Banach Center Publications

The structure of the section space of a real analytic vector bundle on a real analytic manifold X is studied. This is used to improve a result of Grothendieck and Poly on the zero spaces of elliptic operators and to extend a result of Domański and the author on the non-existence of bases to the present case.

Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations

Fabrice Planchon (1999)

Journées équations aux dérivées partielles

We prove that the initial value problem for the semi-linear Schrödinger and wave equations is well-posed in the Besov space B ˙ 2 n 2 - 2 p , ( 𝐑 n ) , when the nonlinearity is of type u p , for p 𝐍 . This allows us to obtain self-similar solutions, as well as to recover previously known results for the solutions under weaker smallness assumptions on the data.

Semicontinuity and continuous selections for the multivalued superposition operator without assuming growth-type conditions

Hông Thái Nguyêñ (2004)

Studia Mathematica

Let Ω be a measure space, and E, F be separable Banach spaces. Given a multifunction f : Ω × E 2 F , denote by N f ( x ) the set of all measurable selections of the multifunction f ( · , x ( · ) ) : Ω 2 F , s ↦ f(s,x(s)), for a function x: Ω → E. First, we obtain new theorems on H-upper/H-lower/lower semicontinuity (without assuming any conditions on the growth of the generating multifunction f(s,u) with respect to u) for the multivalued (Nemytskiĭ) superposition operator N f mapping some open domain G ⊂ X into 2 Y , where X and Y are Köthe-Bochner...

Semicontinuity in L for polyconvex integrals

Emilio Acerbi, Giuseppe Buttazzo, Nicola Fusco (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Viene studiata la semicontinuità rispetto alla topologia di L ( Ω ; 𝐑 m ) per alcuni funzionali del Calcolo delle Variazioni dipendenti da funzioni a valori vettoriali.

Semi-groupes d'opérateurs invariants et opérateurs dissipatifs invariants

Jacques Faraut, Khelifa Harzallah (1972)

Annales de l'institut Fourier

Soit X un espace riemannien symétrique et C 0 ( X ) l’espace des fonctions continues sur X tendant vers 0 à l’infini. On démontre qu’un opérateur ( D A ' , A ) , invariant par les isométries de X , engendre un semi-groupe fortement continu de contractions sur C 0 ( X ) s’il est dissipatif et si son domaine contient les fonctions de classe 𝒞 à support compact.

Semigroups generated by certain pseudo-differential operators on the half-space 0 + n + 1

Victoria Knopova (2004)

Colloquium Mathematicae

The aim of the paper is two-fold. First, we investigate the ψ-Bessel potential spaces on 0 + n + 1 and study some of their properties. Secondly, we consider the fractional powers of an operator of the form - A ± = - ψ ( D x ' ) ± / ( x n + 1 ) , ( x ' , x n + 1 ) 0 + n + 1 , where ψ ( D x ' ) is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator - ( - A ± ) α and prove that with this domain it generates an L p -sub-Markovian semigroup.

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