Fractional integrals over a function of finite type on the intersection spaces

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Let phi be a function of finite type in [-1,1]. We define a fractional integral l(s,phi), over phi by ls,phi f (x) = f1 -1, 1] f (x - phi(t)) dt/vertical bar t vertical bar(s) and prove the (L(p,r) ,L(q))-norm inequalities, where LP. r = L(p) boolean AND L(r), 1/q = s/r + (1 - s)/p, 1 < r <= p <= infinity and 0 < s < 1. For r = 1, we derive the weak-type norm inequality for l(s,phi), provided phi' and phi '' do not vanish. (C) 2011 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2012
Language
English
Article Type
Article
Keywords

WEIGHTED NORM INEQUALITIES; RIESZ-POTENTIALS; MAXIMAL FUNCTIONS; GENERALIZED LEBESGUE; VARIABLE EXPONENT; CURVES; THEOREM

Citation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.387, no.2, pp.1209 - 1218

ISSN
0022-247X
DOI
10.1016/j.jmaa.2011.08.075
URI
http://hdl.handle.net/10203/93977
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