Boundedness of multidimensional Hausdorff operators onH1(Rn)

Boundedness of Multidimensional Dunkl-Hausdorff Operators

“…Hardy Spaces H 1 κ (R n ). Proceeding similarly to the proof of eorem 1 in [13], we are going to extend the earlier version of H 1 estimates, as the strongest and sharp can be found in [4].…”

“…In the one-dimensional case, Hausdorff operators on the real line were introduced in [1] and studied on the Hardy space in [2]. e natural generalization in several dimensions was introduced and studied in [3][4][5]. e reader can see a recent survey article [6] by Liflyand which contains the main results on Hausdorff operators in various settings and bibliography until 2013.…”

Some results for the commutators of generalized Hausdorff operator

“…where A(y) is an n-th order square matrix, which satisfy det A(y) = 0 almost everywhere in the support of Φ ∈ L 1 loc (R n ). Using duality approach, Lerner and Liflayand [22] obtained the boundedness of H Φ,A on real Hardy space H 1 (R n ), after which the same problem was reconsidered in [7,23,31].…”

Hausdorff type operators on the power weighted Hardy spaces H|·|αp(Rn)

“…We notice that the boundedness of on the real Hardy space is extensively studied (see e.g. , , , , ), while there is no any research about the boundedness of on the real Hardy spaces for . On the other hand, when , the boundedness of on is well studied for all (see , , , ).…”