THE BOUNDEDNESS OF CLASSICAL OPERATORS ON VARIABLE L p SPACES
THE BOUNDEDNESS OF CLASSICAL OPERATORS ON VARIABLE L p SPACES
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发表时间：
2006
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通讯作者：
D. Cruz-Uribe;A. Fiorenza;J. M. Martell;C. Pérez
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作者：
D. Cruz-Uribe;A. Fiorenza;J. M. Martell;C. Pérez
我们证明了调和分析|中的许多经典算子，如极大算子、奇异积分、对易子和分数积分|，只要Hardy{Littlewood极大算子在L p（）上有界，它们就在变量Lebesgue空间L p（）上有界。进一步，我们证明了这些算子满足向量值不等式。我们通过应用加权范数不等式和外推理论来做到这一点。作为应用，我们证明了变量Lebesgue空间中4u = f解的Calder on Zygmund不等式，并证明了变量Sobolev空间的Calder on extension定理。
We show that many classical operators in harmonic analysis|such as maximal operators, singular integrals, commutators and fractional integrals|are bounded on the variable Lebesgue space L p( ) whenever the Hardy{Littlewood maximal operator is bounded on L p( ) . Further, we show that such operators satisfy vector-valued inequalities. We do so by applying the theory of weighted norm inequalities and extrapolation. As applications we prove the Calder on{Zygmund inequality for solutions of 4u = f in variable Lebesgue spaces, and prove the Calder on extension theorem for variable Sobolev spaces.