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Studia Mathematica

2008 | 188 | 2 | 123-133

The maximal theorem for weighted grand Lebesgue spaces

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.

123-133

wydano
2008

Twórcy

autor
• 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
• Department of Mathematics, Shivaji College, University of Delhi, Raja Garden, Delhi 110027, India
autor
• Department of Mathematics, Deshbandhu College, University of Delhi, Kalkaji, New Delhi 110019, India