A reconsideration of Hua's inequality. II.
A refinement of an inequality from information theory.
A refinement of Hölder's inequality and applications.
A refinement of Jensen's inequality.
A refinement of Jensen's inequality for a class of increasing and concave functions.
A refinement of the Poincaré inequality for Kolmogorov operators on .
A refinement of van der Corput's inequality.
A refinement of various mean inequalities.
A relation to Hardy-Hilbert's integral inequality and Mulholland's inequality.
A relation to Hilbert's integral inequality and some base Hilbert-type inequalities.
A relationship between intersection conditions and porosity conditions for local systems
A relaxation result in BV for integral functionals with discontinuous integrands
We prove a relaxation theorem in BV for a non coercive functional with linear growth. No continuity of the integrand with respect to the spatial variable is assumed.
A remark on functions continuous on all lines
We prove that each linearly continuous function on (i.e., each function continuous on all lines) belongs to the first Baire class, which answers a problem formulated by K. C. Ciesielski and D. Miller (2016). The same result holds also for on an arbitrary Banach space , if has moreover the Baire property. We also prove (extending a known finite-dimensional result) that such on a separable is continuous at all points outside a first category set which is also null in any usual sense.
A remark on generalized iterates.
A remark on -harmonic functions on Riemannian manifolds.
A remark on linear functions on the sphere
A remark on local fractional calculus and ordinary derivatives
In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.
A remark on the compactness for the Cahn–Hilliard functional
In this note we prove compactness for the Cahn–Hilliard functional without assuming coercivity of the multi-well potential.
A Remark on the Multidimensional Moment Problem.
A remark over the converse of Hölder inequality.