On the norm of an integral operator and applications

By Bicheng Yang. 2006

93 citations recorded by the source corpus.

Abstract In this paper, the norm of an integral operator T : L r ( 0 , ∞ ) → L r ( 0 , ∞ ) ( r > 1 ) is obtained. As applications, a new bilinear integral operator inequality with the norm and the equivalent forms are given, and some new Hilbert's type inequalities with the best constant factors as the particular cases are established.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/78537af033dc773ccfe7d13c86654e47b98a5f77

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In Applied Mathematics

1. Bing He
2. Yongjin Li
3. Michael Th. Rassias
4. Bicheng Yang

Citations in the corpus

• On inequalities of Hilbert's type (2007, methodology): “76 (2007) [1-13] ON INEQUALITIES OF HILBERT'S TYPE YONGJIN Li AND BlNG HE By introducing the function l/(min{x,y}), we establish several new inequalities similar to Hilbert's type inequality.”
• A Hilbert-Type Integral Inequality in the Whole Plane Related to the Hypergeometric Function and the Beta Function (2015, background): “s kernels of degree equal to negative numbers and some parameters is given in [4]. Recently, some inequalities with the homogenous kernels of degree 0 and non-homogenous kernels have been proved (cf. [5]-[10]). Other kinds of Hilbert-type inequalities are shown in [11]-[16]. All of the above integra”