Öppna denna publikation i ny flik eller fönster >>2016 (Engelska)Ingår i: Studia scientiarum mathematicarum Hungarica (Print), ISSN 0081-6906, E-ISSN 1588-2896, Vol. 53, nr 4, s. 545-556Artikel i tidskrift (Refereegranskat) Published
Abstract [en]
In [14] we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H1/(1+α) to the space weak-L1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H1/(1+α), which satisfies the conditions considered in [14], and so that the maximal operators of these Vilenkin—Nörlund means with non-increasing coefficients are not bounded from the Hardy space H1/(1+α) to the space L1/(1+α). In particular, this shows that the conditions under which the result in [14] is proved are in a sense sharp. Moreover, as further applications, some well-known and new results are pointed out.
Nationell ämneskategori
Matematisk analys
Forskningsämne
Matematik
Identifikatorer
urn:nbn:se:ltu:diva-8860 (URN)10.1556/012.2016.53.4.1342 (DOI)000388813600007 ()2-s2.0-84996837296 (Scopus ID)76930bce-6769-4330-b68b-b1c2a6227492 (Lokalt ID)76930bce-6769-4330-b68b-b1c2a6227492 (Arkivnummer)76930bce-6769-4330-b68b-b1c2a6227492 (OAI)
Anmärkning
Validerad; 2016; Nivå 2; 2016-12-05 (inah)
2016-09-292016-09-292018-07-10Bibliografiskt granskad