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As a natural extension of Sobolev spaces, we consider Hardy-Sobolev spaces and establish an atomic decomposition theorem, analogous to the atomic decomposition characterization of Hardy spaces. As an application, we deduce several embedding results for Hardy-Sobolev spaces.
Yong-Kum Cho, and Joonil Kim. "Atomic decomposition on Hardy-Sobolev spaces." Studia Mathematica 177.1 (2006): 25-42. <http://eudml.org/doc/284849>.
@article{Yong2006, abstract = {As a natural extension of $L^\{p\}$ Sobolev spaces, we consider Hardy-Sobolev spaces and establish an atomic decomposition theorem, analogous to the atomic decomposition characterization of Hardy spaces. As an application, we deduce several embedding results for Hardy-Sobolev spaces.}, author = {Yong-Kum Cho, Joonil Kim}, journal = {Studia Mathematica}, keywords = {difference operator; Hardy space; Sobolev space; Sobolev embedding theorem; decomposition; Calderón’s reproducing formula; Hardy-Sobolev space; maximal characterization; Sobolev embedding theorem; Whitney's decomposition lemma}, language = {eng}, number = {1}, pages = {25-42}, title = {Atomic decomposition on Hardy-Sobolev spaces}, url = {http://eudml.org/doc/284849}, volume = {177}, year = {2006}, }
TY - JOUR AU - Yong-Kum Cho AU - Joonil Kim TI - Atomic decomposition on Hardy-Sobolev spaces JO - Studia Mathematica PY - 2006 VL - 177 IS - 1 SP - 25 EP - 42 AB - As a natural extension of $L^{p}$ Sobolev spaces, we consider Hardy-Sobolev spaces and establish an atomic decomposition theorem, analogous to the atomic decomposition characterization of Hardy spaces. As an application, we deduce several embedding results for Hardy-Sobolev spaces. LA - eng KW - difference operator; Hardy space; Sobolev space; Sobolev embedding theorem; decomposition; Calderón’s reproducing formula; Hardy-Sobolev space; maximal characterization; Sobolev embedding theorem; Whitney's decomposition lemma UR - http://eudml.org/doc/284849 ER -