Boundedness of higher-order Marcinkiewicz-Type integrals
2006 ◽
Vol 2006
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pp. 1-21
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Keyword(s):
LetAbe a function with derivatives of ordermandDγA∈Λ˙β(0<β<1,|γ|=m). The authors in the paper proved that ifΩ∈Ls(Sn−1) (s≥n/(n−β))is homogeneous of degree zero and satisfies a vanishing condition, then both the higher-order Marcinkiewicz-type integralμΩAand its variationμ˜ΩAare bounded fromLp(ℝn)toLq(ℝn)and fromL1(ℝn)toLn/(n−β),∞(ℝn), where1<p<n/βand1/q=1/p−β/n. Furthermore, ifΩsatisfies some kind ofLs-Dini condition, then bothμΩAandμ˜ΩAare bounded on Hardy spaces, andμΩAis also bounded fromLp(ℝn)to certain Triebel-Lizorkin space.
2005 ◽
Vol 53
(1)
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pp. 61-73
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1991 ◽
Vol s3-63
(3)
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pp. 595-619
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2017 ◽
Vol 21
(6)
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pp. 1820-1842
1999 ◽
Vol 61
(1)
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pp. 121-128
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2007 ◽
Vol 424
(1)
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pp. 240-281
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1995 ◽
Vol 57
(3)
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pp. 246-253
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