Weighted Inequalities for Integral Operators with Some Homogeneous Kernels
ثبت نشده
چکیده
In this paper we study integral operators of the form Tf(x) = |x − a1y| −α1 . . . |x − amy| mf(y) dy, α1 + . . . + αm = n. We obtain the L (w) boundedness for them, and a weighted (1, 1) inequality for weights w in Ap satisfying that there exists c > 1 such that w(aix) 6 cw(x) for a.e. x ∈ n , 1 6 i 6 m. Moreover, we prove ‖Tf‖BMO 6 c‖f‖∞ for a wide family of functions f ∈ L( ).
منابع مشابه
Weighted Inequalities on Morrey Spaces for Linear and Multilinear Fractional Integrals with Homogeneous Kernels
In this paper, we consider weighted inequalities for linear and multilinear fractional integrals with homogeneous kernels on Morrey spaces. Recently, weighted inequalities without homogeneous kernels were proved by the authors. In this paper, we generalize ones with homogeneous kernels.
متن کاملSharp maximal and weighted estimates for multilinear iterated commutators of multilinear integrals with generalized kernels
In this paper, the authors establish the sharp maximal estimates for the multilinear iterated commutators generated by [Formula: see text] functions and multilinear singular integral operators with generalized kernels. As applications, the boundedness of this kind of multilinear iterated commutators on the product of weighted Lebesgue spaces and the product of variable exponent Lebesgue spaces ...
متن کاملWeighted Norm Inequalities, Off-diagonal Estimates and Elliptic Operators Part Ii: Off-diagonal Estimates on Spaces of Homogeneous Type Pascal Auscher and José
This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a measure of decay. This substitute is that of off-diagonal estimates expressed in terms of local and scale invariant L − L estimates. We propose a definition in spa...
متن کامل2 9 Ju n 20 09 Adams inequalities on measure spaces
In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams’ results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels sati...
متن کاملA ug 2 00 9 Adams inequalities on measure spaces
In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams’ results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels sati...
متن کامل