On the Norm of the Beurling–Ahlfors Operator in Several Dimensions
Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 113-125
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The generalized Beurling–Ahlfors operator $S$ on ${{L}^{p}}({{\mathbb{R}}^{n}};\,\Lambda )$ , where $\Lambda \,:=\,\Lambda ({{\mathbb{R}}^{n}})$ is the exterior algebra with its natural Hilbert space norm, satisfies the estimate $$||S||L\left( {{L}^{p}}\left( {{\mathbb{R}}^{n}};\Lambda\right) \right)\le \left( n/2+1 \right)\left( {{p}^{*}}-1 \right),\,\,\,{{p}^{*}}:=\,\max \{p,\,{{p}^{'}}\}.$$ .This improves on earlier results in all dimensions $n\,\ge \,3$ . The proof is based on the heat extension and relies at the bottom on Burkholder's sharp inequality for martingale transforms.
Hytönen, Tuomas P. On the Norm of the Beurling–Ahlfors Operator in Several Dimensions. Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 113-125. doi: 10.4153/CMB-2010-100-0
@article{10_4153_CMB_2010_100_0,
author = {Hyt\"onen, Tuomas P.},
title = {On the {Norm} of the {Beurling{\textendash}Ahlfors} {Operator} in {Several} {Dimensions}},
journal = {Canadian mathematical bulletin},
pages = {113--125},
year = {2011},
volume = {54},
number = {1},
doi = {10.4153/CMB-2010-100-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-100-0/}
}
TY - JOUR AU - Hytönen, Tuomas P. TI - On the Norm of the Beurling–Ahlfors Operator in Several Dimensions JO - Canadian mathematical bulletin PY - 2011 SP - 113 EP - 125 VL - 54 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-100-0/ DO - 10.4153/CMB-2010-100-0 ID - 10_4153_CMB_2010_100_0 ER -
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