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Here $h(...)$ is a given function and ${\\cal T}_h(...)$ is its given transform, it is independent of $p$. In case when $h\\equiv 1$ we retrieve the well known inequality: (\\int_{\\r} |f^{'}(x)|^pdx \\le (\\sqrt{p-1})^p \\int_{\\r}(\\sqrt{|f^{\"}(x)f(x)|})^pdx.) Our inequalities have form similar to the classical second order Oppial inequalites. 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