Weak-type inequalities for maximal operators acting on Lorentz spaces

Adam Osękowski. "Weak-type inequalities for maximal operators acting on Lorentz spaces." Banach Center Publications 101.1 (2014): 145-162. <http://eudml.org/doc/281906>.

@article{AdamOsękowski2014,
abstract = {We prove sharp a priori estimates for the distribution function of the dyadic maximal function ℳ ϕ, when ϕ belongs to the Lorentz space $L^\{p,q\}$, 1 < p < ∞, 1 ≤ q < ∞. The approach rests on a precise evaluation of the Bellman function corresponding to the problem. As an application, we establish refined weak-type estimates for the dyadic maximal operator: for p,q as above and r ∈ [1,p], we determine the best constant $C_\{p,q,r\}$ such that for any $ϕ ∈ L^\{p,q\}$, $||ℳ ϕ||_\{r,∞\} ≤ C_\{p,q,r\}||ϕ||_\{p,q\}$.},
author = {Adam Osękowski},
journal = {Banach Center Publications},
keywords = {maximal operators; Lorentz spaces; weak-type estimates},
language = {eng},
number = {1},
pages = {145-162},
title = {Weak-type inequalities for maximal operators acting on Lorentz spaces},
url = {http://eudml.org/doc/281906},
volume = {101},
year = {2014},
}

TY - JOUR
AU - Adam Osękowski
TI - Weak-type inequalities for maximal operators acting on Lorentz spaces
JO - Banach Center Publications
PY - 2014
VL - 101
IS - 1
SP - 145
EP - 162
AB - We prove sharp a priori estimates for the distribution function of the dyadic maximal function ℳ ϕ, when ϕ belongs to the Lorentz space $L^{p,q}$, 1 < p < ∞, 1 ≤ q < ∞. The approach rests on a precise evaluation of the Bellman function corresponding to the problem. As an application, we establish refined weak-type estimates for the dyadic maximal operator: for p,q as above and r ∈ [1,p], we determine the best constant $C_{p,q,r}$ such that for any $ϕ ∈ L^{p,q}$, $||ℳ ϕ||_{r,∞} ≤ C_{p,q,r}||ϕ||_{p,q}$.
LA - eng
KW - maximal operators; Lorentz spaces; weak-type estimates
UR - http://eudml.org/doc/281906
ER -