准齐次核的Hilbert型级数不等式取最佳常数因子的等价条件及应用
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摘要
利用实分析技巧及权函数方法,研究了具有准齐次核K(x,y)的Hilbert型级数不等式取最佳常数因子的等价条件,并讨论其在算子理论中的应用.
By using the techinc of real analysis and the way of weight coefficients,the equivalent condition of that Hilbert-type series inequality with this quasi-homogeneous kernel K(x,y)has the best constant factor is obtained,and its applications in the operator theory are discussed.
By using the techinc of real analysis and the way of weight coefficients,the equivalent condition of that Hilbert-type series inequality with this quasi-homogeneous kernel K(x,y)has the best constant factor is obtained,and its applications in the operator theory are discussed.
引文
[1]洪勇,温雅敏.齐次核的Hilbert型级数不等式取最佳常数因子的充要条件[J].数学年刊,2016,37A(3):329-336.
[2]RASSIAS MICHAEL,YANG BICHENG.On a Hardy-Hilbert-type inequality with a general homogeneous kernel[J].Int JNonlinear Anal Appl,2016,7(1):249-269.
[3]洪勇.一类具有准齐次核的涉及多个函数的Hilbert型积分不等式[J].数学学报,2014,57(5):833-840.
[4]和炳,曹俊飞,杨必成.一个全新的多重Hilbert型积分不等式[J].数学学报,2015,58(4):661-672.
[5]YANG BICHENG,CHEN QIANG.Two kinds of Hilbert-type integral inequalities in the whole plane[J/OL].Journal of Inequalities and Applications,2015[2017-12-26].DOI:10.1186/s13660-014-0545-8.
[6]PERIC'I,VUKVIC'P.Hardy-Hilberts inequalities with a general homogeneous kernel[J].Math Inequal Appl,2009,12:525-536.
[7]匡继昌.常用不等式[M].济南:山东科学技术出版社,2004:534-547.
[8]AIZHEN,YANG BICHENG.A more accurate reverse half-discrete Hilbert-type inequality[J/OL].Journal of Inequalities and Applications,2015[2017-12-26].DOI:10.1186/s13660-015-0613-8.
[9]YANG B C,CHEN Q.On a Hardy-Hilbert-type inequality with paremeters[J/OL].Journal of Inequalities and Applications,2015[2017-12-26].DOI:10.1186/s13660-017-1355-6.
[10]YANG BICHENG,CHEN QIANG.A new extension of Hardy-Hilberts inequality in the whole plane[J/OL].Journal of Function Spaces,2016[2017-12-26].Article ID 9197476.
[11]HUANG ZHENXIAO,YANG BICHENG.A multidimensional Hilbert-type integral inequality[J/OL].J Inequalities&Applications,2015[2017-12-26].DOI:10.1186/s13660-015-06173-9.
[2]RASSIAS MICHAEL,YANG BICHENG.On a Hardy-Hilbert-type inequality with a general homogeneous kernel[J].Int JNonlinear Anal Appl,2016,7(1):249-269.
[3]洪勇.一类具有准齐次核的涉及多个函数的Hilbert型积分不等式[J].数学学报,2014,57(5):833-840.
[4]和炳,曹俊飞,杨必成.一个全新的多重Hilbert型积分不等式[J].数学学报,2015,58(4):661-672.
[5]YANG BICHENG,CHEN QIANG.Two kinds of Hilbert-type integral inequalities in the whole plane[J/OL].Journal of Inequalities and Applications,2015[2017-12-26].DOI:10.1186/s13660-014-0545-8.
[6]PERIC'I,VUKVIC'P.Hardy-Hilberts inequalities with a general homogeneous kernel[J].Math Inequal Appl,2009,12:525-536.
[7]匡继昌.常用不等式[M].济南:山东科学技术出版社,2004:534-547.
[8]AIZHEN,YANG BICHENG.A more accurate reverse half-discrete Hilbert-type inequality[J/OL].Journal of Inequalities and Applications,2015[2017-12-26].DOI:10.1186/s13660-015-0613-8.
[9]YANG B C,CHEN Q.On a Hardy-Hilbert-type inequality with paremeters[J/OL].Journal of Inequalities and Applications,2015[2017-12-26].DOI:10.1186/s13660-017-1355-6.
[10]YANG BICHENG,CHEN QIANG.A new extension of Hardy-Hilberts inequality in the whole plane[J/OL].Journal of Function Spaces,2016[2017-12-26].Article ID 9197476.
[11]HUANG ZHENXIAO,YANG BICHENG.A multidimensional Hilbert-type integral inequality[J/OL].J Inequalities&Applications,2015[2017-12-26].DOI:10.1186/s13660-015-06173-9.