Lp(ℝⁿ) boundedness for the commutator of a homogeneous singular integral operator
Guoen Hu
Studia Mathematica, Tome 157 (2003), p. 13-27 / Harvested from The Polish Digital Mathematics Library
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The commutator of a singular integral operator with homogeneous kernel Ω(x)/|x|ⁿ is studied, where Ω is homogeneous of degree zero and has mean value zero on the unit sphere. It is proved that Ω∈L(logL)k+1(Sn-1) is a sufficient condition for the kth order commutator to be bounded on Lp(ℝⁿ) for all 1 < p < ∞. The corresponding maximal operator is also considered.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:284461 
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     title = {$L^{p}(Rn)$ boundedness for the commutator of a homogeneous singular integral operator},
     journal = {Studia Mathematica},
     volume = {157},
     year = {2003},
     pages = {13-27},
     zbl = {1011.42009},
     language = {en},
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Guoen Hu. $L^{p}(ℝⁿ)$ boundedness for the commutator of a homogeneous singular integral operator. Studia Mathematica, Tome 157 (2003) pp. 13-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm154-1-2/