Optimal Hardy–littlewood Type Inequalities for Polynomials and Multilinear Operators
نویسندگان
چکیده
Abstract. In this paper we obtain quite general and definitive forms for Hardy–Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to show that in most cases the exponents involved are optimal. The technique we used is a combination of probabilistic tools and of an interpolative approach; this former technique is also employed in this paper to improve the constants for vectorvalued Bohnenblust–Hille type inequalities.
منابع مشابه
Continuity for Multilinear Integral Operators on Some Hardy and Herz Type Spaces
The continuity for some multilinear operators generated by certain integral operators and Lipschitz functions on some Hardy and Herz-type spaces are obtained. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.
متن کاملEndpoint boundedness for multilinear integral operators of some sublinear operators on Herz and Herz type Hardy spaces
The purpose of this paper is to study the endpoint boundedness properties of some multilinear operators related to certain integral operators on Herz and Herz type Hardy Spaces. The operators include Littlewood-Paley operator and Marcinkiewicz operator.
متن کاملSome sharp inequalities for multilinear integral operators
In this paper, some sharp inequalities for certain multilinear operators related to the Littlewood-Paley operator and the Marcinkiewicz operator are obtained. As an application, we obtain the (L p , L q)-norm inequalities and Morrey spaces boundedness for the multilinear operators.
متن کاملMultiple Weighted Norm Inequalities for Maximal Multilinear Singular Integrals with Non-Smooth Kernels
Weighted norm inequalities for maximal truncated operators of multilinear singular integrals with non-smooth kernels in the sense of Duong, Grafakos, and Yan are obtained; this class of operators extends the class of multilinear CalderónZygmund operators introduced by Coifman and Meyer and includes the higher order commutators of Calderón. The weighted norm inequalities obtained in this work ar...
متن کاملInequalities of Hardy-Littlewood-Polya Type for Functions of Operators and Their Applications
In this paper, we derive a generalized multiplicative Hardy-LittlewoodPolya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of a function of an operator on a class of elements defined with the help of another function of the operator. We then apply the results to solve the following p...
متن کامل