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Sia $K\subset\subset\mathbb{R}^{n}$ un compatto, $f\geq 0$ una funzione analitica all'intorno di $K$ , ed $m$ la massima molteplicità in $K$ degli zeri di $f$ ; si prova che la potenza $f^{\lambda}$ ( $\lambda\in\mathbb{C}$ , $Re\lambda>—\frac{1}{m}$ ) è integrabile in $K$ . L'estensione meromorfa dell'applicazione $\lambda\rightarrow f^{\lambda}$ da $Re\lambda>0$ a tutto $\mathbb{C}$ (con valori in $\mathcal{D}^{\prime}(K)$ anziché in $L^{1}(K)$ ) era già stata provata in [1] e [2].

A remark on E. Green’s paper “Completeness of $L^{p}$ -spaces over finitely additive set functions”

K. P. S. Bhaskara Rao, Vincenzo Aversa (1987)

Colloquium Mathematicae

A remark on Edgar's extremal integral representation theorem

Piotr Mankiewicz (1978)

Studia Mathematica

A remark on extrapolation of rearrangement operators on dyadic $H^{s}$ , 0 < s ≤ 1

Stefan Geiss, Paul F. X. Müller, Veronika Pillwein (2005)

Studia Mathematica

For an injective map τ acting on the dyadic subintervals of the unit interval [0,1) we define the rearrangement operator $T_{s}$ , 0 < s < 2, to be the linear extension of the map $(h_{I}) / {(| I |}^{1 / s}) \mapsto (h_{τ (I)}) (| τ (I) |^{1 / s})$ , where $h_{I}$ denotes the $L^{\infty}$ -normalized Haar function supported on the dyadic interval I. We prove the following extrapolation result: If there exists at least one 0 < s₀ < 2 such that $T_{s ₀}$ is bounded on $H^{s ₀}$ , then for all 0 < s < 2 the operator $T_{s}$ is bounded on $H^{s}$ .

A remark on finite-dimensional $P_{λ}$ -spaces

J. Bourgain (1982)

Studia Mathematica

A remark on functional continuity of certain Fréchet algebras

Helmut Goldmann (1989)

Studia Mathematica

A remark on functions continuous on all lines

Luděk Zajíček (2019)

Commentationes Mathematicae Universitatis Carolinae

We prove that each linearly continuous function $f$ on $ℝ^{n}$ (i.e., each function continuous on all lines) belongs to the first Baire class, which answers a problem formulated by K. C. Ciesielski and D. Miller (2016). The same result holds also for $f$ on an arbitrary Banach space $X$ , if $f$ has moreover the Baire property. We also prove (extending a known finite-dimensional result) that such $f$ on a separable $X$ is continuous at all points outside a first category set which is also null in any usual sense.

A remark on harmonic analysis of strongly almost-periodic groups of linear operators

S. Zaidman (1972)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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