- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:47
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
29
2013
2
Sharp weak type estimates for weights in the class $A_{p_1, p_2}$
Alexander
Reznikov
Vanderbilt University, NASHVILLE, UNITED STATES
Bellman function, $A_{p_1, p_2}$ weight, $A_p$ weight, Muckenhoupt weight, $RH_p$ weight, reverse Hölder condition
We get sharp estimates for the distribution function of nonnegative weights that satisfy the so-called $A_{p_1, p_2}$ condition. For particular choices of parameters $p_1$, $p_2$ this condition becomes an $A_p$-condition or reverse Hölder condition. We also get maximizers for these sharp estimates. We use the Bellman technique and try to carefully present and motivate our tactics. As an illustration of how these results can be used, we deduce the following result: if a weight $w$ is in $A_2$ then it self-improves to a weight that satisfies a reverse Hölder condition.
Fourier analysis
General
433
478
10.4171/RMI/726
http://www.ems-ph.org/doi/10.4171/RMI/726