Semivariation in $L^p$-spaces

Brian Jefferies; Susumu Okada

Displaying similar documents to “Semivariation in $L^{p}$ -spaces”

A zero-two theorem for a certain class of positive contractions in finite dimensional $L^{P}$ -spaces $(1 ⩽ p < + \infty)$

R. Zaharopol (1984)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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Cauchy problem for the complex Ginzburg-Landau type Equation with $L^{p}$ -initial data

Daisuke Shimotsuma, Tomomi Yokota, Kentarou Yoshii (2014)

Mathematica Bohemica

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This paper gives the local existence of mild solutions to the Cauchy problem for the complex Ginzburg-Landau type equation $\frac{\partial u}{\partial t} - (λ + i α) Δ u + (κ + i β) {| u |}^{q - 1} u - γ u = 0$ in $ℝ^{N} \times (0, \infty)$ with $L^{p}$ -initial data $u_{0}$ in the subcritical case ( $1 \leq q < 1 + 2 p / N$ ), where $u$ is a complex-valued unknown function, $α$ , $β$ , $γ$ , $κ \in ℝ$ , $λ > 0$ , $p > 1$ , $i = \sqrt{- 1}$ and $N \in ℕ$ . The proof is based on the $L^{p}$ - $L^{q}$ estimates of the linear semigroup ${exp (t (λ + i α) Δ)}$ and usual fixed-point argument.

On some structural properties of Banach function spaces and boundedness of certain integral operators

T. S. Kopaliani (2004)

Czechoslovak Mathematical Journal

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In this paper the notions of uniformly upper and uniformly lower $ℓ$ -estimates for Banach function spaces are introduced. Further, the pair $(X, Y)$ of Banach function spaces is characterized, where $X$ and $Y$ satisfy uniformly a lower $ℓ$ -estimate and uniformly an upper $ℓ$ -estimate, respectively. The integral operator from $X$ into $Y$ of the form $K f (x) = ϕ (x) \int_{0}^{x} k (x, y) f (y) ψ (y) d y$ is studied, where $k$ , $ϕ$ , $ψ$ are prescribed functions under some local integrability conditions, the kernel $k$ is non-negative and is assumed to satisfy certain...

A note on copies of $c_{0}$ in spaces of weak* measurable functions

Juan Carlos Ferrando (2000)

Commentationes Mathematicae Universitatis Carolinae

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If $(Ω, Σ, μ)$ is a finite measure space and $X$ a Banach space, in this note we show that $L_{w^{*}}^{1} (μ, X^{*})$ , the Banach space of all classes of weak* equivalent $X^{*}$ -valued weak* measurable functions $f$ defined on $Ω$ such that $∥ f (ω) ∥ \leq g (ω)$ a.e. for some $g \in L_{1} (μ)$ equipped with its usual norm, contains a copy of $c_{0}$ if and only if $X^{*}$ contains a copy of $c_{0}$ .

Displaying similar documents to “Semivariation in L p -spaces”

A zero-two theorem for a certain class of positive contractions in finite dimensional L P -spaces ( 1 ⩽ p &lt; + ∞ )

Cauchy problem for the complex Ginzburg-Landau type Equation with L p -initial data

On some structural properties of Banach function spaces and boundedness of certain integral operators

A note on copies of c 0 in spaces of weak* measurable functions

Displaying similar documents to “Semivariation in $L^{p}$ -spaces”

A zero-two theorem for a certain class of positive contractions in finite dimensional $L^{P}$ -spaces $(1 ⩽ p < + \infty)$

Cauchy problem for the complex Ginzburg-Landau type Equation with $L^{p}$ -initial data

A note on copies of $c_{0}$ in spaces of weak* measurable functions