tailieunhanh - báo cáo hóa học: " Boundedness of positive operators on weighted amalgams"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Boundedness of positive operators on weighted amalgams | Aguilar Canestro and Ortega Salvador Journal of Inequalities and Applications 2011 2011 13 3 Journal of Inequalities and Applications http content 2011 1 13 a SpringeiOpen Journal RESEARCH Open Access Boundedness of positive operators on weighted amalgams María Isabel Aguilar Canestro and Pedro Ortega Salvador Correspondence portega@uma. es Análisis Matemático Facultad de Ciencias Universidad de Málaga 29071 Málaga Spain Abstract In this article we characterize the pairs u v of positive measurable functions such that T maps the weighted amalgam Lp v q in Lp u lq for all 1 p q p q x where T belongs to a class of positive operators which includes Hardy operators maximal operators and fractional integrals. 2000 Mathematics Subject Classification 26D10 26D15 42B35 Keywords Amalgams Maximal operators Weighted inequalities Weights 1. Introduction Let u be a positive function of one real variable and let p q 1. The amalgam Lp u lq is the space of one variable real functions which are locally in Lp u and globally in lq. More precisely Lp u q f Ilfllp u q x where llfllp u q - q n 1 p Ị If Ipu 1 q ugZ n These spaces were introduced by Wiener in 1 . The article 2 describes the role played by amalgams in Harmonic Analysis. Carton-Lebrun Heinig and Hoffmann studied in 3 the boundedness of the Hardy operator Pf x - f-m If I in weighted amalgam spaces. They characterized the pairs of weights u v such that the inequality IlPf p u q Cllf p v q holds for all f with a constant C independent of f whenever 1 q q X . The characterization of the pairs u v for to hold in the case 1 q q TO has been recently completed by Ortega and Ramirez 4 who have also characterized the weak type inequality pf w . C f p v q SpringerOpen0 2011 Canestro and Salvador licensee Springer. This is an Open Access article distributed underthe terms of the Creative Commons Attribution License http licenses by which permits unrestricted