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摘要
We establish sufficient conditions on the weight functions u and v for the validity of the multidimensional weighted inequality
integral(E)Phi(T(k)f(x))(q)u(x) dx (1/q) <= C integral(E)Phi(f(x))(p)v(x) dx (1/p),
where 0 < p, q < infinity, Phi is a logarithmically convex function, and T(k) is an integral operator over star-shaped regions. The condition is also necessary for the exponential integral inequality. Moreover, the estimation of C is given and we apply the obtained results to generalize some multidimensional Levin-Cochran-Lee type inequalities.
- 出版日期2010-6
