Interpolation of operators

By Colin Bennett, R. Sharpley. 1987

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Citations in the corpus

Consistent Kernel Mean Estimation for Functions of Random Variables (2016, background): “Thus Theorem V.1.12 of Bennett and Sharpley (1988) applies and gives the desired inclusion.”
Density Estimation in Infinite Dimensional Exponential Families (2013, methodology): “Then, for x ∈ E 0 + E 1 := { x 0 + x 1 : x 0 ∈ E 0 , x 1 ∈ E 1 } and t > 0, the K -functional of the real interpolation method, see [4, Deﬁnition 1.1, p. 293], is deﬁned by Suppose E and F are two Banach spaces that satisfy F ֒ E (i.e., F ⊂ E and the inclusion operator id : F → E is continuous),…”
Basic properties of strong mixing conditions. A survey and some open questions (2005, methodology): “” Then one can apply results and techniques from functional analysis, including interpolation theory (see [1] or [8]), to efficiently compare those measures of dependence and derive a broad class of “covariance inequalities.”
Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, background): “Besov classes also arise via real interpolations of L p(Rn) and W 1,p(Rn), see for example [20,93].”
Estimating a Convex Function in Nonparametric Regression (2007, background): “The main idea is similar to the concept of nondecreasing rearrangements (see Ryff, 1965, 1970; Bennett & Sharpely, 1988).”
A direct approach to the duality of grand and small Lebesgue spaces (2009, background): “[2]) f ∗(t) = inf{λ > 0 : |{x ∈ (0, 1) : |f(x)| > λ}| ≤ t} ∀t ∈ [0, 1] (here the convention inf ∅ = +∞ is adopted; the symbol |E| denotes, for any measurable set E ⊂ (0, 1), its Lebesgue measure).”
Isomorphic copies in the lattice E and its symmetrization E(∗) with applications to Orlicz–Lorentz spaces (2009, background): “In particular, the notions related to Schauder bases, basic sequences or related to the theory of lattices are analogous to the corresponding notions in Banach spaces or Banach lattices which can be found in [2,3,5,25,27,28,41].”
Optimal Gaussian Sobolev embeddings (2009, background): “Properties (P1) and (P2) are satisfied thanks to standard properties of the decreasing rearrangement (see [8]).”
Series of independent random variables in rearrangement invariant spaces: An operator approach (2005, methodology): “( s e e [BS], Lemma 4.”
Remarks on Gagliardo–Nirenberg type inequality with critical Sobolev space and BMO (2008, methodology): “3, we make use of the following proposition by Bennett–Sharpley [4].”
The predual and John-Nirenberg inequalities on generalized BMO martingale spaces (2014, background): “ohn-Nirenberg inequality and something else, the space BMO (Bounded Mean Oscillation; see [6], [7] and [12]) played a remarkable role in classical analysis and probability. We refer to the monograghs [3] and [20] for the function space version, respectively to the monograghs [2], [8] and [18] for th”
Adams’ Inequality and Limiting Sobolev Embeddings into Zygmund Spaces (2012, background): “2 Preliminaries We recall some basic definitions, for which our main reference is [6].”
Singular integrals and potentials in some Banach function spaces with variable exponent (2003, background): “For definition and fundamental properties of Banach function space we refer to [2].”