Martingales and sharp bounds for Fourier multipliers (Q2906165)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Martingales and sharp bounds for Fourier multipliers |
scientific article; zbMATH DE number 6077179
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Martingales and sharp bounds for Fourier multipliers |
scientific article; zbMATH DE number 6077179 |
Statements
Martingales and sharp bounds for Fourier multipliers (English)
0 references
5 September 2012
0 references
Fourier multiplier
0 references
Riesz transform
0 references
martingale transform
0 references
differential subordination
0 references
\textit{S. Geiss, S. Montgomery-Smith} and \textit{E. Saksman} [Trans. Am. Math. Soc. 362, No. 2, 553--575 (2010; Zbl 1196.60078)] characterized the \(L_p\)-norm of the second order Riesz transforms \(R_iR_j\). This result is generalized here, the \(L_p\)-norms of certain Fourier multipliers are identified. As a special case the \(L_p\)-norm of \(\sum_{i,j=1,\dots ,d}a_{i,j}R_iR_j\) is given. Similar results are obtained for Levy multipliers.
0 references
