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Results tagged with sobolev-spaces
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user 153260
A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
3
votes
Accepted
Is the local maximal function bounded from $W^{1, 1}$ to $L^1$?
Yes I think this is true.
Let $\mathcal{G} := \{ \times_{i=1}^n[k_i,k_i+1] : k_i\in \mathbb{Z} \} $ be the grid of cubes of side length $1$ and vertices in $ \mathbb{Z}^n$. For $Q\in \mathcal{G} $ le …
3
votes
$L^p$ domination of mixed partial derivatives by the unmixed ones?
It should be true for $p>1$. For a function $\varphi$ in the Schwartz class it holds that \begin{equation}
D_1D_2 \varphi(x) = -R_1 R_2 \Delta \varphi(x),
\end{equation}
where $R_1, R_2$ are the Riesz …
4
votes
$L^p$ domination of mixed partial derivatives of the 3rd order by the unmixed ones?
I think similar questions always translate in the $L^p$ boundedness of a Fourier multiplier. In this case you want a Fourier multiplier which "exchanges the operator $D_1D_2D_3$ with the operator $D_1 …