The maximal theorem for weighted grand Lebesgue spaces

• Autorzy: Alberto Fiorenza , Babita Gupta , Pankaj Jain
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26D15: Inequalities for sums, series and integrals
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 188
• Numer: 2
• Strony: 123-133

Daty

wydano

2008

Twórcy

autor

Alberto Fiorenza

• Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università di Napoli, via Monteoliveto 3, 80134 Napoli, Italy
• Istituto per le Applicazioni del Calcolo "Mauro Picone", Sezione di Napoli, Consiglio Nazionale delle Ricerche, via Pietro Castellino 111, 80131 Napoli, Italy

autor

Babita Gupta

• Department of Mathematics, Shivaji College, University of Delhi, Raja Garden, Delhi 110027, India

autor

Pankaj Jain

• Department of Mathematics, Deshbandhu College, University of Delhi, Kalkaji, New Delhi 110019, India

Identyfikatory

DOI

10.4064/sm188-2-2