Related papers: Interpolation theorem for anisotropic net spaces

We present a new, elementary proof of Boyd's interpolation theorem. Our approach naturally yields a noncommutative version of this result and even allows for the interpolation of certain operators on l^1-valued noncommutative symmetric…

This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…

We give a formula of the Upsilon invariant of any L-space cable knot $K_{p,q}$ using $p,\Upsilon_K$ and $\Upsilon_{T_{p,q}}$. The integral value of the Upsilon invariant gives a ${\mathbb Q}$-valued knot concordance invariant. We compute…

We develop a constructive piecewise polynomial approximation theory in weighted Sobolev spaces with Muckenhoupt weights for any polynomial degree. The main ingredients to derive optimal error estimates for an averaged Taylor polynomial are…

Let $\vec{X}=(X_0, X_1)$ be a compatible couple of Banach spaces, $ 1\le p \le \infty$ and let $ \varphi$ be positive quasi-concave function. Denote by $\overline{X}_{\varphi,p}=(X_0,X_1)_{\varphi,p}$ the real interpolation spaces defined…

The Modified Quasichemcial Model in the Distinguishable-Pair Approximation (MQMDPA) for manifold short-range orders in liquids has been successfully extended to multicomponent solutions. The extension is conducted by means of the…

The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…

We study a class of interacting particle systems with asymmetric interaction showing a self-duality property. The class includes the ASEP($q,\theta$), asymmetric exclusion process, with a repulsive interaction, allowing up to $\theta\in…

Let $\alpha\in\mathbb{R}$, $p\in[1,\infty)$, $q\in(0,\infty]$, $\mathbf{W}$ be a matrix weight, and $A$ be an expansive dilation on $\mathbb{R}^d$. In this paper, the authors firstly investigate and develop some aspects of homogeneous…

This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…

We show that, for certain non-smooth bounded domains $\Omega\subset\mathbb{R}^n$, the real interpolation space $(L^p(\Omega), W^{1,p}(\Omega))_{s,p}$ is the subspace $\widetilde W^{s,p}(\Omega) \subset L^p(\Omega)$ induced by the restricted…

We prove noncommutative Khintchine inequalities for all interpolation spaces between $L_p$ and $L_2$ with $p<2$. In particular, it follows that Khintchine inequalities hold in $L_{1,\infty}$. Using a similar method, we find a new…

This is a continuation of the papers [Kuryakov-Sukochev, JFA, 2015] and [Sadovskaya-Sukochev, PAMS, 2018], in which the isomorphic classification of $L_{p,q}$, for $1< p<\infty$, $1\le q<\infty$, $p\ne q $, on resonant measure spaces, has…

We show that the Chern-Schwartz-MacPherson class of a hypersurface X in a nonsingular variety M `interpolates' between two other notions of characteristic classes for singular varieties, provided that the singular locus of X is smooth and…

We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…

In 1967, Peetre proposed to give a precise description of the real interpolation space for Besov hierarchical spaces $l^{s,q}(A)$. In 1974, Cwikel proved that the Lions-Peetre formula for $(l^{q_0}(A_0), l^{q_1}(A_1))_{\theta,r}$ have no…

We study complex interpolation of variable Triebel-Lizorkin spaces, especially we present the complex interpolation of $F_{p(\cdot),q}^{\alpha }$ and $F_{p(\cdot ),p(\cdot )}^{\alpha (\cdot )}$ spaces. Also, some limiting cases are given.

First, we consider some fundamental properties including dual spaces, complex interpolations of $\alpha$-modulation spaces $M^{s,\alpha}_{p,q}$ with $0<p,q \le \infty$. Next, necessary and sufficient conditions for the scaling property and…

Let $0<p<q\leq\infty$ and $\alpha \in (0,\infty]$. We give a characterization of quasi-Banach interpolation spaces for the couple $(L_p(0,\alpha),L_q(0,\alpha))$ in terms of two monotonicity properties, extending known results which mainly…

We prove a weighted version of a classical inequality of Johnson and Schechtman from which we derive a decomposition theorem for $p$-th moments ($0<p\leq 1$) of nonnegative generalized $U$-statistics with constant not dependent on $p$. In…