Premium
On the Boundedness and Compactness of a Class of Integral Operators
Author(s) -
Prokhorov Dmitrii V.
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461079900856x
Subject(s) - compact space , mathematics , operator (biology) , locally integrable function , integrable system , class (philosophy) , maximal operator , function (biology) , pure mathematics , mathematical analysis , combinatorics , bounded function , artificial intelligence , computer science , biochemistry , chemistry , repressor , evolutionary biology , biology , transcription factor , gene
Let α > 0. The operator of the formT α f ( x ) = υ ( x )x α∫ 0 xf ( y ) d y( x ‐ y )1 ‐ α,x > 0 ,is considered, where the real weight function v ( x ) is locally integrable on R + := (0, ∞). In case v ( x ) = 1 the operator coincides with the Riemann–Liouville fractional integral, L p → L q estimates of which with power weights are well known. This work gives L p → L q boundedness and compactness criteria for the operator T α in the case 0 < p , q < ∞, p > max(1/α, 1).