A new approach to boundary trace inequalities for Sobolev functions is presented, which reduces any trace inequality involving general rearrangement-invariant norms to an equivalent, considerably simpler, one-dimensional inequality for a Hardy-type operator. In particular, improvements of classical boundary trace embeddings and new optimal trace embeddings are derived.

By using the way of weight coefficients, the technique of real analysis, and Hermite-Hadamard's inequality, a more accurate Hardy-Mulholland-type inequality with multi-parameters and a best possible constant factor is given. The equivalent forms, the reverses, the operator expressions and some particular cases are considered.

In this paper we study the integrability properties of a general version of the Boltzmann collision operator that includes inelastic interactions between particles. We prove a Young’s inequality for variable hard potentials, a Hardy-Littlewood-Sobolev inequality for soft potentials, and estimates with Maxwellian weights for variable hard potentials. In addition we obtain sharp constants for Max...

By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.

In this paper, by using the Euler-Maclaurin expansion for the zeta function and estimating the weight function effectively, we derive a strengthenment of a Hardy-Hilbert’s type inequality proved by W.Y. Zhong. As applications, some particular results are considered.

where x = (y, z) ∈ R × R was studied by Badiale and Tarantello in [1]. Our aim is to solve two open problems contained in [1]. First we compute the optimal value of the constant C in Equation (1) in the case of Hardy’s inequality, namely p = q = β. In fact we prove a more general inequality with optimal constant in Section 2. In Section 3, we consider the symmetry of the optimal functions. Usin...

We consider the series expansion of [Formula: see text]-Hardy inequality [G. Barbatis, S. Filippas and A. Tertikas, Series for text] Hardy inequalities, Indiana Univ. Math. J. 52 (2003) 171–190], in particular case where distance is taken from an interior point a bounded domain text]. For we improve it by adding as remainder term optimally weighted critical Sobolev norm, generalizing result [S....

Consider the second order divergence form elliptic operator L with complex bounded coefficients. In general, the operators related to it (such as Riesz transform or square function) lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we generalize the classical approach and develop a theory of Hardy and ...

We give improvements and generalizations of both the classical Hardy inequality geometric based on divergence theorem. Especially, our improved type derives two inequalities with best constants. Besides, we improve Rellich by using inequality.

Consider a second order divergence form elliptic operator L with complex bounded coefficients. In general, operators related to it (such as the Riesz transform or square function) lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includ...