# Questions tagged [interpolation-spaces]

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### Interpolation space between $L^1\cap L^2$ and $L^1$

In the paper of Bourgain, the way equation (3.78) is deduced from (3.69) and (3.76) seems via the following interpolation result. Let $(X,\mu)$ and $(Y,\nu)$ be two measure spaces and let $T$ be a ...
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### Real interpolation of weighted Sobolev spaces with different weights

Let $\Omega \subseteq \mathbb{R}^n$ be open and let $w_0$ and $w_1$ be measurable and almost everywhere positive and finite functions defined on $\Omega$. Let $L^2_{w_0}(\Omega)$ be the weighted ...
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### Interpolation functional for BV spaces?

Recently, while trying to tackle a problem, I found that it would be convenient that I could find some sort of 'interpolation theorem' for Bounded Variation Spaces. More specifically, let's define, ...
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### The real method of interpolation and operator ideals

Let $\overline{A} \mbox{ and } \overline{B}$ be n+1-tuples of Banach spaces and $T:\overline{A}\rightarrow \overline{B}$ be an interpolation operator; let $J(\overline{A})$ and (the corresponding, ...
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### What is $(L^2(M), H^1_0(M))_{\frac 12}$ on a smooth manifold with boundary?

Let $M$ be a smooth compact manifold. If $M$ is closed, we have that the interpolation space $$(L^2(M), H^1(M))_{\frac 12}=H^{\frac 12}(M)$$ (see Taylor's book on PDE for example). Suppose $M$ has a ...
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### Traces of fractional Sobolev spaces $W^{s,p}$ with $0<s<1/p$

I've stumbled upon a problem involving the trace of a function in a fractional Sobolev space of the form $W^{s,2}(H)$, where $H$ is a half-plane in $\mathbb{R}^2$. Would it be possible to define a ...
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### Interpolation of the row and column operator spaces

If $R$ and $C$ are respectively the row and column operator spaces, and $\theta \in (0, 1)$, we denote by $R(\theta)$ the interpolation operator space $(R, C)_{\theta}$ (with $R(0) = R$ and $R(1) = C$)...
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### About norm on $H^{\frac 12}(M \times \{0,1\})$

Let $X=M \times \{0,1\}$ with $M$ a smooth compact manifold without boundary. Define the fractional Sobolev space $H^{\frac 12}(X) = (L^2(X), H^1(X))_{\frac 12}$, as the real interpolation space ...
### Interpolation between $L_p$ and $B^s_{q,q}$
I am looking for a reference or a direct argument that shows the real interpolation space between $L_p$ and $B^s_{q,q}$ is $B^\alpha_{r,r}$, with the usual conditions on the indices. This result is ...