ar X iv : m at h / 05 05 57 4 v 1 [ m at h . FA ] 2 6 M ay 2 00 5 On the boundedness the Marcinkiewicz operator on multipliers space By Sadek Gala
نویسنده
چکیده
Let h(y) be a bounded radial function and Ω (y ′) an H 1 function on the unit sphere satisfying the cancelation condition. Then the Marcinkiewicz integral operator µ Ω related to the Littlewood-Paley g−function is defined by µ Ω (f)(x) = ∞ 0 |F t (x)| 2 dt t 3 1 2 , (1) where F t (x) = |x−y|≤t Ω (x − y) |x − y| d−1 h (|x − y|) f (y)dy (2) and h(y) ∈ L ∞ (R +). In this paper, we prove that the operator µ Ω is bounded on multipliers spaces X r R d = M H r → L 2. Moreover, we give also the boundedness for a class of Marcinkiewicz integral operators with rough kernels µ * Ω,λ and µ Ω,S related to the Littlewood-Paley g * λ −function and the area integral S, respectively. Our results are substantial improvents and extensions of known results on the Marcinkiewicz integral operator introduced by E.M. Stein.
منابع مشابه
ar X iv : m at h / 05 02 57 3 v 6 [ m at h . A G ] 1 4 M ay 2 00 6 ON DEFORMATIONS OF FLAG
Any (global) deformation of a flag manifold F with b2 = 1 is biholomorphic to F .
متن کاملar X iv : m at h / 05 05 51 6 v 1 [ m at h . G N ] 2 4 M ay 2 00 5 HEREDITY OF τ - PSEUDOCOMPACTNESS
S. Garćıa-Ferreira and H. Ohta gave a construction that was intended to produce a τ -pseudocompact space, which has a regular-closed zero set A and a regular-closed C-embedded set B such that neither A nor B is τ pseudocompact. We show that although their sets A, B are not regular-closed, there are at least two ways to make their construction work to give the desired example.
متن کاملar X iv : m at h / 06 05 64 5 v 1 [ m at h . A G ] 2 4 M ay 2 00 6 ON NORI ’ S FUNDAMENTAL GROUP SCHEME
The aim of this note is to give two structure theorems on Nori’s fundamental group scheme of a proper connected variety defined over a perfect field and endowed with a rational point.
متن کاملar X iv : m at h / 06 05 37 9 v 1 [ m at h . R A ] 1 5 M ay 2 00 6 AN EXTENDED FREUDENTHAL MAGIC SQUARE IN CHARACTERISTIC 3
Date: May 15, 2006. 2000 Mathematics Subject Classification. Primary 17B25.
متن کامل