Persistence properties for the Fokas-Olver-Rosenau-Qiao equation in weighted L p $L^{p}$ spaces

A Note on Weighted Composition Operators on L^p-Spaces

BANACH SPACES EMBEDDING ISOMETRICALLY INTO Lp WHEN 0<p<l

For 0 < p < 1 we give examples of Banach spaces isometrically embedding into Lp but not into any Lr with p < r < 1.

Breakdown for the Camassa-Holm Equation Using Decay Criteria and Persistence in Weighted Spaces

We exhibit a sufficient condition in terms of decay at infinity of the initial data for the finite time blowup of strong solutions to the Camassa–Holm equation: a wave breaking will occur as soon as the initial data decay faster at infinity than the solitons. In the case of data decaying slower than solitons we provide persistence results for the solution in weighted L-spaces, for a large class...

Complex interpolation of weighted noncommutative Lp-spaces

Let M be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace τ . Let d be an injective positive measurable operator with respect to (M, τ ) such that d is also measurable. Define Lp(d) = {x ∈ L0(M) : dx+ xd ∈ Lp(M)} and ‖x‖Lp(d) = ‖dx+ xd‖p . We show that for 1 6 p0 < p1 6 ∞, 0 < θ < 1 and α0 > 0, α1 > 0 the interpolation equality (Lp0(d 0), Lp1(d α))θ = Lp(d ) hol...

Maximal regularity for evolution equations in weighted Lp - spaces

LetX be a Banach space and let A be a closed linear operator on X. It is shown that the abstract Cauchy problem u̇(t)+ Au(t) = f (t), t > 0, u(0) = 0, enjoys maximal regularity in weighted Lp-spaces with weights ω(t) = tp(1−μ), where 1/p < μ, if and only if it has the property of maximal Lp-regularity. Moreover, it is also shown that the derivation operator D = d/dt admits anH∞-calculus in weigh...