1,360 research outputs found
Rubio de Francia's extrapolation theory: estimates for the distribution function
Let be an arbitrary operator bounded from into for every weight in the Muckenhoupt class . It is
proved in this article that the distribution function of with respect to
any weight can be essentially majorized by the distribution function of
with respect to (plus an integral term easy to control). As a
consequence, well-known extrapolation results, including results in a
multilinear setting, can be obtained with very simple proofs. New applications
in extrapolation for two-weight problems and estimates on rearrangement
invariant spaces are established too.Comment: 29 page
A multiplier theorem using the Schechter's method of interpolation
AbstractLet m be a measurable bounded function and let us assume that there exists a bounded functions S so that m(Ī¾)S(Ī¾)itā1 is a Fourier multiplier on Lp uniformly in tāR. Then, using the analytic interpolation theorem of Stein, one can show that necessarily m is a Lp multiplier. The purpose of this work is to show that under the above conditions, it holds that, for every kāN, m(logS)kāMp. The technique is based on the Schechter's interpolation method
New Extrapolation Estimates
AbstractGiven a sublinear operator T satisfying that āTĻAāLp(Ī½)ā©½Cpā1āĻAāLp(Ī¼), for every measurable set A and every 1<pā©½p0, with C independent of A and p, we show that supr>0ā«ā1/rĪ»Ī½Tf(y)dy1+log+rā²ā«M|f(x)|(1+log+|f(x)|)dĪ¼(x). This estimate allows us to improve Yano's extrapolation theorem and also to obtain that for every fāLlogL(Ī¼), rāāā«ā1/rĪ»Ī½Tf(y)dylogrā²āfā1. Other types of extrapolation results are also given
Modified Gravity at Astrophysical Scales
Using a perturbative approach we solve stellar structure equations for
low-density (solar-type) stars whose interior is described with a polytropic
equation of state in scenarios involving a subset of modified gravity theories.
Rather than focusing on particular theories, we consider a model-independent
approach in which deviations from General Relativity are effectively described
by a single parameter . We find that for length scales below those set by
stellar General Relativistic radii the modifications introduced by modified
gravity can affect the computed values of masses and radii. As a consequence,
the stellar luminosity is also affected. We discuss possible further
implications for higher density stars and observability of the effects before
described.Comment: 12 pages, 7figures, matches published versio
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