We prove a multi-parameter Hilbert-type integral inequality with a hybrid kernel. We describe the best constant in the inequality in terms of hypergeometric functions. Some equivalent forms of the inequalities are also studied. By specifying parameter values we obtain results proved by other authors as well as many new inequalities.
Given a strongly continuous semigroup on a Banach space X with generator A and an element f ∈ D(A²) satisfying and for all t ≥ 0 and some ω > 0, we derive a Landau type inequality for ||Af|| in terms of ||f|| and ||A²f||. This inequality improves on the usual Landau inequality that holds in the case ω = 0.
We present a new Marchaud type inequality in spaces.
2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.Certain types of weighted Peetre K-functionals are characterized by means of the classical moduli of smoothness taken on a proper linear transforms of the function. The weights with power-type asymptotic at the ends of the interval with arbitrary real exponents are considered. This paper extends the method and results presented...