# Weak-type inequalities for maximal operators acting on Lorentz spaces

Banach Center Publications (2014)

- Volume: 101, Issue: 1, page 145-162
- ISSN: 0137-6934

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topAdam 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 -

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