Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

The maximal theorem for weighted grand Lebesgue spaces

100%

Fiorenza A., Gupta B., Jain P.

Studia Mathematica

2008

tom 188

nr 2

123-133

We study the Hardy inequality and derive the maximal theorem of Hardy and Littlewood in the context of grand Lebesgue spaces, considered when the underlying measure space is the interval (0,1) ⊂ ℝ, and the maximal function is localized in (0,1). Moreover, we prove that the inequality $||Mf||_{p),w} ≤ c||f||_{p),w}$ holds with some c independent of f iff w belongs to the well known Muckenhoupt class $A_{p}$, and therefore iff $||Mf||_{p,w} ≤ c||f||_{p,w}$ for some c independent of f. Some results of similar type are discussed for the case of small Lebesgue spaces.

Ograniczanie wyników

1 Studia Mathematica

1 Fiorenza A.

1 Gupta B.

1 Jain P.

1 2008

Wyniki wyszukiwania

The maximal theorem for weighted grand Lebesgue spaces