On ψ- interpolation spaces

By L. Nikolova, T. Zachariades. 2009

2,440 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9eec8f9d105314313ed6d463c87e7733341dbb1c

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Citations in the corpus

Banach frames for α-modulation spaces (2007, background): “3 and by applying standard arguments of complex interpolation of mixed norm sequence spaces [3], matrices in Aα,(1−α)γ,η are also bounded on p,q m (Z2) for suitable s.”
Decay estimates for a class of wave equations (2008, background): “Some properties of these function spaces can be found in [2, 16].”
Continuous dependence for NLS in fractional order spaces (2010, background): “See for example [1,23] for the definitions of these spaces and the corresponding Sobolev’s embeddings.”
Anisotropic Hardy-Lorentz spaces and their applications (2015, methodology): “It is well known that (L1(R), L(R))θ,q = L (R) and (L1(R), L(R))θ,q = L (R), where p ∈ (0,∞), 0 < q1 ≤ q2 ≤ ∞, q ∈ [q1, q2] and θ ∈ (0, 1) satisfying that 1/q = (1− θ)/q1 + θ/q2 (see [8]).”
WEIGHTED ENERGY-DISSIPATION FUNCTIONALS FOR GRADIENT FLOWS (2011, methodology): “Let us refer to [4] for notation and results on real interpolation between Banach spaces, in particular for the definition of (C([0, T ];H), H(1)(0, T ;H))η,1 which is used in the following result.”
The Bohr radius of the $n$-dimensional polydisk is equivalent to $\sqrt{\frac{\log n}{n}} (2013, neutral): “It is well-known (see [1,3]) that if p,q ∈ [1,+∞)m and θ ∈ (0, 1), then [lp, lq]θ = lr with 1 ri = θ pi + 1−θ qi for 1 ≤ i ≤ m.”
Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, neutral): “[3]) this leads to ( L ,D( √ L) ) θ,q = (Lp,D(√L)2m) θθ0,q = Aspq, s = 2θθ0m = θr.”
Regularity of Stochastic Kinetic Equations (2016, methodology): “4 in [BL76] we have for 0 ≤ s0 < s1 ≤ 2, θ ∈ (0, 1), p ≥ 2, (H0 p (R ), H1 p (R ))θ,p = B s p,p(R ) (18) with s = (1− θ)s0 + θs1.”
On an Extreme Class of Real Interpolation Spaces (2009, background): “Monographs by Butzer and Berens [6], Bergh and Löfström [5], Triebel [36], Beauzamy [2], Bennett and Sharpley [4], Connes [18] and Amrein, Boutet de Monvel and Georgescu [1] illustrate this fact.”
The Hörmander multiplier theorem for multilinear operators (2012, background): “Multilinear interpolation ([7], [1]) yields that Tσ is bounded from Lp1(Rn)× · · · × Lpm(Rn) to Lp(Rn) for all indices pj satisfying 1 < p1, .”
Well-posedness for Semi-relativistic Hartree Equations of Critical Type (2005, background): “But as a direct consequence of the Milhin multiplier theorem [BL76], the cited result holds for Ds := (μ2 − ∆)s/2, where μ ≥ 0 is a fixed constant.”
A new proof of long-range scattering for critical nonlinear Schrödinger equations (2010, neutral): “(5)L denotes the usual Lorentz space [3].”