Author:
Hong Yong,Feng Mingjun,He Bing
Abstract
UDC 517.9
By using the inverse Hölder inequality and the weight function method, we establish the inverse Hilbert-type integral inequality. In the case of a quasihomogeneous kernel, we obtain the necessary and sufficient conditions for the optimal matching parameters. Finally, their applications in the operator theory are discussed.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Reference10 articles.
1. Y. Hong, C. Wu, Q. Chen, Matching parameter conditions for the best Hilbert-type integral inequality with a class of non-homogeneous kernels, J. Jilin Univ. (Sci. Ed.), 59, № 2, 208–212 (2021).
2. B. He, Y. Hong, Q. Chen, The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications, Open Math., 19, 400–411 (2021).
3. Q. Chen, B. He, Y. Hong, Z. Li, Equivalent parameter conditions for the validity of half-discrete Hilbert-type multiple integral inequality with generalized homogeneous kernel, J. Funct. Space, Article ID 7414861 (2020).
4. Y. Hong, Q. Huang, Q. Chen, The parameter conditions for the existence of the Hilbert-type multiple integral inequality and its best constant factor, Ann. Funct. Anal., 12, № 7 (2021); https://doi.org/10.1007/s43034-020-00087-5.
5. Q. Chen, B. Yang, A reverse Hardy–Hilbert-type integral inequality involving one derivative function, J. Inequal. and Appl., 2020, Article 259 (2020).