Weak- and strong-type inequality for the cone-like maximal operator in variable Lebesgue spaces

Title:

Weak- and strong-type inequality for the cone-like maximal operator in variable Lebesgue spaces

Creator:

Szarvas, Kristóf and Weisz, Ferenc

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:e415d73b-defa-4866-bbd4-ef121044225e
uuid:e415d73b-defa-4866-bbd4-ef121044225e
issn:0011-4642

Subject:

matematika, Lebesgueovy prostory, nerovnosti (matematika), mathematics, Lebesgue spaces, inequalities (mathematics), variable Lebesgue space maximal operator γ-rectangle Besicovitch’s covering theorem weak-type inequality strong-type inequality, maximal operator, γ-rectangle, Besicovitch’s covering theorem, weak-type inequality, strong-type inequality, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

The classical Hardy-Littlewood maximal operator is bounded not only on the classical Lebesgue spaces Lp(Rd) (in the case p > 1), but (in the case when 1/p(·) is log-Hölder continuous and p- = inf{p(x): x\in Rd > 1) on the variable Lebesgue spaces Lp(·)(Rd), too. Furthermore, the classical Hardy-Littlewood maximal operator is of weak-type (1, 1). In the present note we generalize Besicovitch’s covering theorem for the so-called γ-rectangles. We introduce a general maximal operator Msγδ, and with the help of generalized Φ-functions, the strong- and weak-type inequalities will be proved for this maximal operator. Namely, if the exponent function 1/p(·) is log-Hölder continuous and p- ≥ s, where 1 ≤ s ≤ ∞ is arbitrary (or p- ≥ s), then the maximal operator Msγδ is bounded on the space Lp(·)(Rd) (or the maximal operator is of weak-type (p(·), p(·)))., Kristóf Szarvas, Ferenc Weisz., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1079-1101

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:4

Harvested from:

CDK

Metadata only:

false