Boundedness of composition operators associated with mixed homogeneities on Lipschitz spaces

The Boundedness of Calderón–Zygmund Operators on Lipschitz Spaces Over Spaces of Homogeneous Type

“…It was well known that on Euclidean space R n the dual space of Fefferman and Stein 1972). Notice that the classical Lipschitz spaces on R n play an important role in harmonic analysis and partial differential equations (see Han and Han 2016;Krantz 1982).…”

Boundedness of composition operators with mixed homogeneities

“… introduced a class of Hardy spaces which have a multi‐parameter structure with underlying mixed homogeneities arising from T 1 and T 2 under consideration, and obtained the boundedness of the composition operator on the Hardy space . For more results about composition operators, see also .…”

“…Han, Lin et al [7] introduced a class of Hardy spaces which have a multi-parameter structure with underlying mixed homogeneities arising from 1 and 2 under consideration, and obtained the boundedness of the composition operator 1 • 2 on the Hardy space . For more results about composition operators, see also [4][5][6]12]. A natural question arise: If 1 and 2 are non-convolution Calderón-Zygmund operators with isotropic and non-isotropic homogeneities, respectively, is the composition operator 1 • 2 bounded on the Hardy space ?…”

$Tb$ criteria for Calderon--Zygmund operators on Lipschitz spaces with para-accretive functions

“…, and the norm of f is defined by f Lip b (α) = g Lip(α) . Notice that the classical Lipschitz spaces on R n play an important role in harmonic analysis and partial differential equations (see [6], [11]- [13], [17]).…”