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A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.

Petteri Harjulehto, Peter Hästö (2004)

Revista Matemática Complutense

We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e.g. if the exponent p is continuous in the closure of a convex domain. We also give an essentially sharp condition for the exponent p as to when there exists an imbedding from the Sobolev space to the space of bounded functions.

A comparative analysis of Bernstein type estimates for the derivative of multivariate polynomials

Szilárd Gy. Révész (2006)

Annales Polonici Mathematici

We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in a domain where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses in a convex domain K. The other, pluripotential-theoretic approach, mainly due to Baran, works for even more general sets, and uses the pluricomplex Green function (the Zaharjuta-Siciak extremal function). When the inscribed ellipse method...

A local Landau type inequality for semigroup orbits

Gerd Herzog, Peer Christian Kunstmann (2014)

Studia Mathematica

Given a strongly continuous semigroup ( S ( t ) ) t 0 on a Banach space X with generator A and an element f ∈ D(A²) satisfying | | S ( t ) f | | e - ω t | | f | | and | | S ( t ) A ² f | | e - ω t | | A ² f | | 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.

A New Characterization of Weighted Peetre K-Functionals (II)

Draganov, Borislav, Ivanov, Kamen (2007)

Serdica Mathematical Journal

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...

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