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It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space to . This implies the almost everywhere convergence of the Fejér means in a cone for all , which is larger than .
Ferenc Weisz. "Multi-dimensional Fejér summability and local Hardy spaces." Studia Mathematica 194.2 (2009): 181-195. <http://eudml.org/doc/284861>.
@article{FerencWeisz2009, abstract = {It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space $W(h_\{p\},ℓ_\{∞\})$ to $W(L_\{p\},ℓ_\{∞\})$. This implies the almost everywhere convergence of the Fejér means in a cone for all $f ∈ W(L₁,ℓ_\{∞\})$, which is larger than $L₁(ℝ^\{d\})$.}, author = {Ferenc Weisz}, journal = {Studia Mathematica}, keywords = {Wiener amalgam spaces; local Hardy spaces; Fejér summability; Fourier transforms; atomic decomposition}, language = {eng}, number = {2}, pages = {181-195}, title = {Multi-dimensional Fejér summability and local Hardy spaces}, url = {http://eudml.org/doc/284861}, volume = {194}, year = {2009}, }
TY - JOUR AU - Ferenc Weisz TI - Multi-dimensional Fejér summability and local Hardy spaces JO - Studia Mathematica PY - 2009 VL - 194 IS - 2 SP - 181 EP - 195 AB - It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space $W(h_{p},ℓ_{∞})$ to $W(L_{p},ℓ_{∞})$. This implies the almost everywhere convergence of the Fejér means in a cone for all $f ∈ W(L₁,ℓ_{∞})$, which is larger than $L₁(ℝ^{d})$. LA - eng KW - Wiener amalgam spaces; local Hardy spaces; Fejér summability; Fourier transforms; atomic decomposition UR - http://eudml.org/doc/284861 ER -