Some tauberian theorems for weighted means of double integrals on R2+
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
Let p(x) and q(y) be nondecreasing continuous functions on [0, ?) such that p(0) = q(0) = 0 and p(x), q(y) ? ? as x, y ? ?. For a locally integrable function f(x, y) on R 2 + = [0, ?) × [0, ?), we denote its double integral by F(x, y) = ? x 0 ? y 0 f(t, s)dtds and its weighted mean of type (?, ?) by t?,?(x, y) = ? x 0 ? y 0 ( 1 ? p(t) p(x) )? ( 1 ? q(s) q(y) )? f(t, s)dtds where ? > ?1 and ? > ?1. We say that ? ? 0 ? ? 0 f(t, s)dtds is integrable to L by the weighted mean method of type (?, ?) determined by the functions p(x) and q(x) if limx,y?? t?,?(x, y) = L exists. We prove that if limx,y?? t?,?(x, y) = L exists and t?,?(x, y) is bounded on R 2 + for some ? > ?1 and ? > ?1, then limx,y?? t?+h,?+k(x, y) = L exists for all h > 0 and k > 0. Finally, we prove that if ? ? 0 ? ? 0 f(t, s)dtds is integrable to L by the weighted mean method of type (1, 1) determined by the functions p(x) and q(x) and conditions p(x) p ? (x) ? y 0 f(x, s)ds = O(1) and q(y) q ? (y) ? x 0 f(t, y)dt = O(1) hold, then limx,y?? F(x, y) = L exists.
Açıklama
Anahtar Kelimeler
Divergent integrals, Weighted means of double integrals, Tauberian theorems and conditions
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Fındık, G., Çanak, İ. (2019). Some tauberian theorems for weighted means of double integrals on R2+. International Conference of Mathematical Sciences. s. 030019(1)-030019(3).
