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Results tagged with reference-request
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user 153260
This tag is used if a reference is needed in a paper or textbook on a specific result.
4
votes
1
answer
432
views
Reference or proof of a theorem of L. Fejér on summability of Fourier series
In the article "Ensembles exceptionnels" by A. Beurling, the author cites the following theorem of Fejér:
Suppose that a $2\pi$ periodic function $ f $, Lebesgue integrable in $(0,2\pi)$ satisfies the …
5
votes
Accepted
Is Toeplitz operator on the Bergman space bounded iff its symbol is bounded?
It is not neccesary in general that $\varphi \in L^\infty(\mathbb{D})$, but it is necessary and sufficient
that in a certain sense $\varphi$ must be bounded ``on average in the hyperbolic sense''. The …
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 …
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 …