Sharp Marchaud and Converse Inequalities in Orlicz Spaces
نویسندگان
چکیده
For Lp spaces on Td, Rd and Sd−1 sharp versions of the classical Marchaud inequality are known. These results are extended here to Orlicz spaces (on Td, Rd and Sd−1) for which M(u1/q) is convex for some q, 1 < q ≤ 2, where M(u) is the Orlicz function. Sharp converse inequalities for such spaces are deduced.
منابع مشابه
Sharp conditions for Korn inequalities in Orlicz spaces
We show that Korn’s inequality in Orlicz spaces holds if and only if the Orlicz function satisfies the ∆2and the ∇2-condition. This result applies to several types of Korn’s inequality. In particular we show that Korn’s inequality is false in L, in L logL, in Exp and in L∞. MSC (2000): 74 B, 74 G, 76 D, 49 J.
متن کاملMartingale Inequalities in Exponential Orlicz Spaces
A result is found which is similar to BDG-inequalities, but in the framework of exponential (non moderate) Orlicz spaces. A special class of such spaces is introduced and its properties are discussed with respect to probability measures, whose densities are connected by an exponential model. Acknowledgement: Thanks are due to Prof. M. Mania (Georgian Academy of Sciences) for the discussions and...
متن کاملOrlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces
We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see text]. We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequen...
متن کاملPolynomial Approximation and ω rφ ( f , t ) Twenty Years Later
About twenty years ago the measure of smoothness ω φ (f, t) was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time. MSC: 41A10, 41A17, 41A25, 41A27, 41A30, 41A36, 41A40, 41A50, 41A63, 26A15, 26B35, 26B05, 42C05, 26A51, 26A33, 46E35 keywords: Moduli of smoothness, K-functionals, realization functi...
متن کاملTwenty Years Later
About twenty years ago the measure of smoothness ω φ (f, t) was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time. MSC: 41A10, 41A17, 41A25, 41A27, 41A30, 41A36, 41A40, 41A50, 41A63, 26A15, 26B35, 26B05, 42C05, 26A51, 26A33, 46E35 keywords: Moduli of smoothness, K-functionals, realization functi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005