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On certain nonstandard Calderón-Zygmund operators

100%

Hofmann S.

Studia Mathematica

1994

tom 109

nr 2

105-131

We formulate a version of the T1 theorem which enables us to treat singular integrals whose kernels need not satisfy the usual smoothness conditions. We also prove a weighted version. As an application of the general theory, we consider a class of multilinear singular integrals in $ℝ^n$ related to the first Calderón commutator, but with a kernel which is far less regular.

A weak molecule condition for certain Triebel-Lizorkin spaces

100%

Hofmann S.

Studia Mathematica

1991-1992

tom 101

nr 2

113-122

A weak molecule condition is given for the Triebel-Lizorkin spaces Ḟ_p^{α,q}, with 0 < α < 1 and 1 < p, q < ∞. As an easy corollary, one may deduce, by atomic-molecular methods, a Triebel-Lizorkin space "T1" Theorem of Han and Sawyer, and Han, Jawerth, Taibleson and Weiss, for Calderón-Zygmund kernels K(x,y) which are not assumed to satisfy any regularity condition in the y variable.

Ograniczanie wyników

2 Studia Mathematica

2 Hofmann S.

1 1994

1 1992

Wyniki wyszukiwania

On certain nonstandard Calderón-Zygmund operators

A weak molecule condition for certain Triebel-Lizorkin spaces