BOUNDEDNESS OF THE FRACTIONAL INTEGRAL ON WEIGHTED LEBESGUE AND LIPSCHITZ-SPACES

Authors
HARBOURE E SALINAS O VIVIANI B
Citation
E. Harboure et al., BOUNDEDNESS OF THE FRACTIONAL INTEGRAL ON WEIGHTED LEBESGUE AND LIPSCHITZ-SPACES, Transactions of the American Mathematical Society, 349(1), 1997, pp. 235-255
Citations number
12
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
349
Issue
1
Year of publication
1997
Pages
235 - 255
Database
ISI
SICI code
0002-9947(1997)349:1<235:BOTFIO>2.0.ZU;2-3
Abstract
Necessary and sufficient conditions are given for the fractional integ ral operator I-alpha to be bounded from weighted strong and weak L(p) spaces within the range p greater than or equal to n/alpha into suitab le weighted BMO and Lipschitz spaces. We also characterize the weights for which I-alpha can be extended to a bounded operator from weighted BMO into a weighted Lipschitz space of order alpha. Finally, under an additional assumption on the weight, we obtain necessary and sufficie nt conditions for the boundedness of I-alpha between weighted Lipschit z spaces.