Abstract
We prove a generalization of the pointwise Stein inequality, considering two truncated versions. More generally than in the Stein inequality, we assume that the kernel is dominated by a radial function almost decreasing after the division by a power function with nonnegative exponent in the case of the truncation to the ball of the radius and almost increasing after the multiplication by a power function in the case of truncation to the exterior of this ball. We give some applications to a series of inequalities of Hardy type in norms of various function spaces, in particular, in the norm of variable exponent Lebesgue spaces $$ {L^{p\left( \cdot \right)}}\left( {{{\mathbb{R}}^n}} \right) $$ with weights. Bibliography: 40 titles.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.