Series expansion of Leray–Trudinger inequality

In this paper, we establish an infinite series expansion of Leray–Trudinger inequality, which is closely related with Hardy inequality and Moser Trudinger inequality. Our result extends early results obtained by Mallick and Tintarev [A. Mallick and C. Tintarev. An improved Leray-Trudinger inequality. Commun. Contemp. Math. 20 (2018), 17501034. OP 21] to the case with many logs. It should be pointed out that our result is about series expansion of Hardy inequality under the case $p=n$ , which case is not considered by Gkikas and Psaradakis in [K. T. Gkikas and G. Psaradakis. Optimal non-homogeneous improvements for the series expansion of Hardy's inequality. Commun. Contemp. Math. doi:10.1142/S0219199721500310]. However, we can't obtain the optimal form by our method.

Factorization of Cesàro operator and related inequalities

In this paper, we introduce two factorizations for the Cesàro matrix of order n based on Cesàro and gamma matrices. The results of these factorizations are new inequalities, one of which is a generalized version of the well-known Hardy’s inequality. Moreover, we obtain the norm of Cesàro operator of order n on Cesàro and gamma matrix domains.

Generalizations of Integral Inequalities Similar to Hardy’s Inequality

In this paper, we established the generalizations of integral inequalities similar to Hardy’s inequality. Keywords: Hardy’s inequality; Integral inequalities; similar version; Hlder’s inequality; Generalizations

Generalizations of Hardy Type Inequalities by Abel–Gontscharoff’s Interpolating Polynomial

In this paper, we extend Hardy’s type inequalities to convex functions of higher order. Upper bounds for the generalized Hardy’s inequality are given with some applications.