A Calderon - Zygmund extension theorem for abstract
نویسنده
چکیده
It is shown that if the Boyd indices of the rearrangement invariant Banach function space Lρ(R) are strictly between 0 and 1, ρ is an absolutely continuous function norm, Ω is a domain from R satisfying the restricted cone condition, denoting by ω the restriction of ρ to Ω, there exists an extension operator for the abstract Sobolev space W Lω(Ω). This is a generalization to abstract Sobolev spaces of a result obtained by de Souza for Orlicz-Sobolev spaces.
منابع مشابه
Wavelet Decomposition of Calderon - Zygmund Operators on Function Spaces
We make use of the Beylkin-Coifman-Rokhlin wavelet decomposition algorithm on the CalderonZygmund kernel to obtain some fine estimates on the operator and prove the T(\) theorem on Besov and Triebel-Lizorkin spaces. This extends previous results of Frazier et at., and Han and Hofmann. 2000 Mathematics subject classification: primary 42B20, 46B30.
متن کاملA Simple Proof of the Sharp Weighted Estimate for Calderon-zygmund Operators on Homogeneous Spaces
Here we show that Lerner’s method of local mean oscillation gives a simple proof of theA2 conjecture for spaces of homogeneous type: that is, the linear dependence on the A2 norm for weighted L 2 Calderon-Zygmund operator estimates. In the Euclidean case, the result is due to Hytönen, and for geometrically doubling spaces, Nazarov, Rezinikov, and Volberg obtained the linear bound.
متن کاملInterpolation of Linear Operators
The aim of this paper is to prove a generalization of a well-known convexity theorem of M. Riesz [8]. The Riesz theorem was originally deduced by "real-variable" techniques. Later, Thorin [10], Tamarkin and Zygmund [9], and Thorin [ll] introduced convexity properties of analytic functions in their study of Riesz's theorem. These ideas were put in especially suggestive form by A. P. Calderon and...
متن کاملSingular Integrals on Hilbert Space
exists as a bounded operator on L(H) as ô tends to zero and p tends to infinity. A theorem of this type extends the Calderon-Zygmund theory of singular integral operators on En to infinite dimensions. For if fc(#)||x||-" is a Calderon-Zygmund kernel and if £ is a bounded Borel set which is disjoint from a neighborhood of the origin then v{E) =fEk(x)\\x\\~ dx satisfies v(tE) = v(E) for £>0; if g...
متن کاملAcademy of Sciences of the Czech Republic
We study the Oseen problem with rotational effect in exterior three-dimensional domains. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces in the whole three-dimensional space. As the main tool we derive and apply an inequality of the FriedrichsPoincaré type and the theory of Calderon-Zygmund kernels in weighted spaces. For the ex...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006