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Necessary and Sufficient Conditions and Optimal Constant Factors for the Validity of Multiple Integral Half-Discrete Hilbert Type Inequalities with a Class of Quasi-Homogeneous Kernels
Bing He,Yong Hong,Bicheng Yang
Keywords:Quasi homogeneous kernel, half-discrete Hilbert type inequality, equivalence condition, best constant factor, boundedness of operator.
Abstract:
      The problem of equivalence parameters and the best constant factor for the existence of quasi-homogeneous half-discrete Hilbert type inequality $$\int_{\mathbb{R}_{+}^{m}} \sum_{n=1}^{\infty} G\left( n^{\lambda_1}/ \|x\|^{\lambda_2}_{\rho}\right) a_{n} f(x) \mathrm{d} x \leq M\|\tilde{a}\|_{p, \alpha}\|f\|_{q, \beta}$$ is discussed, and their applications in the study of operator boundedness and norm are also considered.