On weighted multidimensional embeddings for monotone functions

Authors

  • Sorina Barza
  • Lars-Erik Persson
  • Vladimir D. Stepanov

DOI:

https://doi.org/10.7146/math.scand.a-14328

Abstract

We characterize the inequality 7817 \left(\int_{\mathbf{R}^N_+} f^q u\right)^{1/q} \leq C \left(\int_{\mathbf{R}^N_+} f^p v \right)^{1/p},\,\,0<q ,p <\infty, 7817 for monotone functions $f\geq 0$ and nonnegative weights $u$ and $v$. The case $q < p$ is new and the case $0<p\leq q <\infty$ is extended to a modular inequality with N- functions. A remarkable fact concerning the calculation of $C$ is pointed out.

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Published

2001-06-01

How to Cite

Barza, S., Persson, L.-E., & Stepanov, V. D. (2001). On weighted multidimensional embeddings for monotone functions. MATHEMATICA SCANDINAVICA, 88(2), 303–319. https://doi.org/10.7146/math.scand.a-14328

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Section

Articles