Abstract
Let d ≥ 2 and let η : Rd - 1 → R be a smooth function which is supported in [- 1, 1]d - 1. Suppose μ is the measure on Rd given byμ (E) = under(∫, Rd - 1) χE (x, φ (x)) η (x) d x with φ (x) = ∑i = 1d - 1 ± | xi |ai, 1 ≠ ai ∈ R. In this paper we study the Lp-Lq estimates for singular fractional integral operators given byA f (x) = under(∫, Rd) f (x - y) (underover(∏, i = 1, d - 1) | yi |γi - 1) d μ (y) with 0 < γi.
Original language | English |
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Pages (from-to) | 407-417 |
Number of pages | 11 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 332 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2007 Aug 1 |
Externally published | Yes |
Keywords
- Fractional integral operator
ASJC Scopus subject areas
- Analysis
- Applied Mathematics