126,299 research outputs found
Estimates for the maximal singular integral in terms of the singular integral:the case of even kernels
The purpose of this paper is to describe the smooth homogeneous
Calderon-Zygmund operators for which the maximal singular integral T*f may be
controlled by the singular integral Tf. We consider two types of control. The
first is the L2 estimate of T*f by Tf, namely the estimate of the L2 norm of
T*f by a constant times the L2 norm of Tf. The second is the pointwise estimate
of T*f(x) by a constant times M(Tf)(x), where M denotes the Hardy-Littlewood
maximal operator. Notice that this is an improved variant of Cotlar's
inequality, because the term Mf(x) is missing on the right hand side. Our main
result states that, for even operators, both are equivalent to a purely
algebraic condition formulated in terms of the expansion of the kernel in
spherical harmonics. The condition holds by higher order Riesz transforms,
which then satisfy an improved version of Cotlar's inequalityComment: Minor misprints and English inaccuracies corrected, references
updated. To appear in Annals on Mat
Lp and weak L1 estimates for the maximal Riesz transform and the maximal Beurling transform
We estimate in Lp the maximal Riesz transform in terms of the Riesz transform
itself for p greater than 1. In the limiting case p=1 the weak L1 inequality is
shown to fail. Surprisingly, the weak L1 inequality for the maximal Beurling
transform in terms of the Beurling transform does hold.Comment: 12 page
Beltrami equation with coefficient in Sobolev and Besov spaces
Our goal in this work is to present some function spaces on the complex plane
\C, X(\C), for which the quasiregular solutions of the Beltrami equation,
, have first derivatives locally in
X(\C), provided that the Beltrami coefficient belongs to X(\C)
Capacities associated with scalar signed Riesz kernels, and analytic capacity
The real and imaginari parts of the Cauchy kernel in the plane are scalar
Riesz kernels of homogeneity -1. One can associate with each of them a natural
notion of capacity related to bounded potentials. The main result of the paper
asserts that these capacities are comparable to classical analytic capacity,
thus stressing the real variables nature of analytic capacity. Higher
dimensional versions of this result are also considered.Comment: 37 pages, ams.or
On rotating doubly connected vortices
In this paper we consider rotating doubly connected vortex patches for the
Euler equations in the plane. When the inner interface is an ellipse we show
that the exterior interface must be a confocal ellipse. We then discuss some
relations, first found by Flierl and Polvani, between the parameters of the
ellipses, the velocity of rotation and the magnitude of the vorticity in the
domain enclosed by the inner ellipse.Comment: 30 page
A new characterization of Sobolev spaces on
In this paper we present a new characterization of Sobolev spaces on
Euclidian spaces (). Our characterizing condition is obtained via
a quadratic multiscale expression which exploits the particular symmetry
properties of Euclidean space. An interesting feature of our condition is that
depends only on the metric of and the Lebesgue measure, so that
one can define Sobolev spaces of any order of smoothness on any metric measure
space.Comment: Two references added. Some statements have been improved and proofs
made clearer. Typos correcte
estimates for the maximal singular integral in terms of the singular integral
This paper continues the study, initiated in the works {MOV} and {MOPV}, of
the problem of controlling the maximal singular integral by the
singular integral . Here is a smooth homogeneous Calder\'on-Zygmund
singular integral operator of convolution type. We consider two forms of
control, namely, in the weighted norm and via pointwise estimates
of by or \,, where is the Hardy-Littlewood
maximal operator and its iteration. The novelty with respect to
the aforementioned works, lies in the fact that here is different from 2
and the space is weighted
The maximal Beurling transform associated with squares
It is known that the improved Cotlar's inequality ,
, holds for the Beurling transform , the maximal Beurling
transform , , and the Hardy--Littlewood maximal operator . In this note we consider
the maximal Beurling transform associated with squares, namely,
, ,
being the square with sides parallel to the coordinate axis
of side length . We prove that ,
, where is the iteration of the
Hardy--Littlewood maximal operator, and cannot be replaced by .Comment: 3 figure
A Note on Transport Equation in Quasiconformally Invariant Spaces
In this note, we study the well-posedness of the Cauchy problem for the
transport equation in the BMO space and certain Triebel-Lizorkin spaces.Comment: 14 page
Invariant Algebraic Slicing of the Spacetime
Using the momentum constraint, the standard evolution system is written in a
fully first order form. The class of first order invariant algebraic slicing
conditions is considered. The full set of characteristic fields is explicitly
given. Characteristic speeds associated to the gauge dependent eigenfields
(gauge speeds) are related to light speed.Comment: 4 pages, uuencoded gzip-compressed ps file. Also available at
http://jean-luc.ncsa.uiuc.edu/Papers/ To appear in the ERE (Menorca, Spain,
Sept 94) 94 proceeding
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