Geodesic
Mapping properties of integral averaging operators
Studia Mathematica, Tome 129 (1998) no. 2, pp. 157-177 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Characterizations are obtained for those pairs of weight functions u and v for which the operators $Tf(x) = ʃ_{a(x)}^{b(x)} f(t)dt$ with a and b certain non-negative functions are bounded from $L^p_u(0,∞)$ to $L^q_v(0,∞)$, 0 p,q ∞, p≥ 1. Sufficient conditions are given for T to be bounded on the cones of monotone functions. The results are applied to give a weighted inequality comparing differences and derivatives as well as a weight characterization for the Steklov operator.
DOI : 10.4064/sm-129-2-157-177
Keywords: integral averaging operator, weight characterizations, Hardy inequalities, Steklov operator, differences 
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H. P.  Heinig;  . Mapping properties of integral averaging operators. Studia Mathematica, Tome 129 (1998) no. 2, pp. 157-177. doi: 10.4064/sm-129-2-157-177

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