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

T. S. Kopaliani

Displaying similar documents to “On some structural properties of Banach function spaces and boundedness of certain integral operators”

Semivariation in $L^{p}$ -spaces

Brian Jefferies, Susumu Okada (2005)

Commentationes Mathematicae Universitatis Carolinae

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Suppose that $X$ and $Y$ are Banach spaces and that the Banach space $X {\hat{\otimes}}_{τ} Y$ is their complete tensor product with respect to some tensor product topology $τ$ . A uniformly bounded $X$ -valued function need not be integrable in $X {\hat{\otimes}}_{τ} Y$ with respect to a $Y$ -valued measure, unless, say, $X$ and $Y$ are Hilbert spaces and $τ$ is the Hilbert space tensor product topology, in which case Grothendieck’s theorem may be applied. In this paper, we take an index $1 \leq p < \infty$ and suppose that $X$ and $Y$ are $L^{p}$ -spaces with $τ_{p}$ the associated...

A Pythagorean approach in Banach spaces.

Gao, Ji (2006)

Journal of Inequalities and Applications [electronic only]

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Ergodic properties of contraction semigroups in $L_{p}$ , $1 < p < \infty$

Ryotaro Sato (1994)

Commentationes Mathematicae Universitatis Carolinae

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Let ${T (t) : t > 0}$ be a strongly continuous semigroup of linear contractions in $L_{p}$ , $1 < p < \infty$ , of a $σ$ -finite measure space. In this paper we prove that if there corresponds to each $t > 0$ a positive linear contraction $P (t)$ in $L_{p}$ such that $| T (t) f | \leq P (t) | f |$ for all $f \in L_{p}$ , then there exists a strongly continuous semigroup ${S (t) : t > 0}$ of positive linear contractions in $L_{p}$ such that $| T (t) f | \leq S (t) | f |$ for all $t > 0$ and $f \in L_{p}$ . Using this and Akcoglu’s dominated ergodic theorem for positive linear contractions in $L_{p}$ , we also prove multiparameter pointwise ergodic and local ergodic...

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.

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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Displaying similar documents to “On some structural properties of Banach function spaces and boundedness of certain integral operators”

Semivariation in L p -spaces

A Pythagorean approach in Banach spaces.

Ergodic properties of contraction semigroups in L p , 1 < p < ∞

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

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

Semivariation in $L^{p}$ -spaces

Ergodic properties of contraction semigroups in $L_{p}$ , $1 < p < \infty$

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

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