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We prove an analogue of Y. Meyer's wavelet characterization of the Hardy space H¹(ℝⁿ) for the space H¹(ℝⁿ,X) of X-valued functions. Here X is a Banach space with the UMD property. The proof uses results of T. Figiel on generalized Calderón-Zygmund operators on Bochner spaces and some new local estimates.
Tuomas Hytönen. "Vector-valued wavelets and the Hardy space H¹(ℝⁿ,X)." Studia Mathematica 172.2 (2006): 125-147. <http://eudml.org/doc/286376>.
@article{TuomasHytönen2006, abstract = {We prove an analogue of Y. Meyer's wavelet characterization of the Hardy space H¹(ℝⁿ) for the space H¹(ℝⁿ,X) of X-valued functions. Here X is a Banach space with the UMD property. The proof uses results of T. Figiel on generalized Calderón-Zygmund operators on Bochner spaces and some new local estimates.}, author = {Tuomas Hytönen}, journal = {Studia Mathematica}, keywords = {Hardy space; wavelet basis; atomic decomposition; generalized Calderón-Zygmund operators; UMD space}, language = {eng}, number = {2}, pages = {125-147}, title = {Vector-valued wavelets and the Hardy space H¹(ℝⁿ,X)}, url = {http://eudml.org/doc/286376}, volume = {172}, year = {2006}, }
TY - JOUR AU - Tuomas Hytönen TI - Vector-valued wavelets and the Hardy space H¹(ℝⁿ,X) JO - Studia Mathematica PY - 2006 VL - 172 IS - 2 SP - 125 EP - 147 AB - We prove an analogue of Y. Meyer's wavelet characterization of the Hardy space H¹(ℝⁿ) for the space H¹(ℝⁿ,X) of X-valued functions. Here X is a Banach space with the UMD property. The proof uses results of T. Figiel on generalized Calderón-Zygmund operators on Bochner spaces and some new local estimates. LA - eng KW - Hardy space; wavelet basis; atomic decomposition; generalized Calderón-Zygmund operators; UMD space UR - http://eudml.org/doc/286376 ER -