New retarded integral inequalities with applications.
New strengthened Carleman's inequality and Hardy's inequality.
New upper and lower bounds for the Čebyšev functional.
New upper bounds for Mathieu-type series.
New variants of Khintchine's inequality.
Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.
New weighted multivariate Grüss type inequalities.
New weighted Poincaré-type inequalities for differential forms.
Newer applications of generalized monotone sequences.
Newton's inequalities for families of complex numbers.
Nonlinear delay discrete inequalities and their applications to Volterra type difference equations.
Nonlinear delay integral inequalities for piecewise continuous functions and applications.
Nonlinear integral inequalities in two independent variables on time scales.
Nonlinear integral inequalities in two independent variables and their applications.
Nonlinear integral inequality in two independent variables.
Nonlinear singular integral inequalities for functions in two and independent variables.
Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds
Let G be a real connected Lie group with polynomial volume growth endowed with its Haar measuredx. Given a C² positive bounded integrable function M on G, we give a sufficient condition for an L² Poincaré inequality with respect to the measure M(x)dx to hold on G. We then establish a nonlocal Poincaré inequality on G with respect to M(x)dx. We also give analogous Poincaré inequalities on Riemannian manifolds and deal with the case of Hardy inequalities.
Norm comparison inequalities for the composite operator.
Norm estimates for Bessel-Riesz operators on generalized Morrey spaces
We revisit the properties of Bessel-Riesz operators and present a different proof of the boundedness of these operators on generalized Morrey spaces. We also obtain an estimate for the norm of these operators on generalized Morrey spaces in terms of the norm of their kernels on an associated Morrey space. As a consequence of our results, we reprove the boundedness of fractional integral operators on generalized Morrey spaces, especially of exponent , and obtain a new estimate for their norm.
Norm inequalities for integral operators on cones
Norm inequalities in weighted amalgam
Hardy inequalities for the Hardy-type operators are characterized in the amalgam space which involves Banach function space and sequence space.