Abstract
We introduce a class of integral operators related to parametric Marcinkiewicz operators. We present a multiplier formula characterizing the L2 boundedness of such class of operators. Also, we prove L p-β (inhomogeneous Sobolev space)→Lp estimates provided that the kernels are in L(logL)(Sn-1). In fact, we show that the global parts of the introduced operators are bounded on the Lebesgue spaces Lp(1 < p < ∞) while the local parts are bounded on certain Sobolev spaces Lp-β.
Original language | English |
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Pages (from-to) | 56-81 |
Number of pages | 26 |
Journal | Communications in Mathematical Analysis |
Volume | 13 |
Issue number | 2 |
Publication status | Published - 2012 |
Externally published | Yes |
Keywords
- Bessel functions
- Fourier transform
- Marcinkiewicz integrals
- Rough integral operators
- Sobolev spaces
- Triebel-Lizorkin space
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics