MAPPING PROPERTIES OF THE MARCINKIEWICZ INTEGRALS ON HOMOGENEOUS GROUPS

Title & Authors
MAPPING PROPERTIES OF THE MARCINKIEWICZ INTEGRALS ON HOMOGENEOUS GROUPS
Choi, Young-Woo; Rim, Kyung-Soo;

Abstract
Under the cancellation property and the Lipschitz condition on kernels, we prove that the Marcinkiewicz integrals defined on a homogeneous group H are bounded from $\small{H^1}$(H) to $\small{L^1}$(H), from $\small{L_{c}}$ $\small{^{\infty}}$(H) to BMO (H), and from $\small{L^{p}}$ (H) to $\small{L^{p}}$ (H) for 1 < p < $\small{\infty}$ assuming the $\small{L^{q}}$ -boundedness for some q > 1.for some q > 1.
Keywords
Marcinkiewicz integrals;homogeneous groups;
Language
English
Cited by
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