The theory of orlicz spaces plays a crucial role in a very wide spectrum see. In section 6, we present its noncommutative analogue in terms of conditional. Pdf applications of the theory of orlicz spaces to vector. Multiplicity of solutions for nonhomogeneous neumann problems in orliczsobolev spaces shapour heidarkhani, massimiliano ferrara, giuseppe caristi, johnny henderson, amjad salari communicated by mokhtar kirane abstract. Why are orlicz spaces useful for statistical physics. A brief introduction to nfunctions and orlicz function spaces john alexopoulos kent state university, stark campus.
Section 4 is a sketch of the basic theory of orlicz spaces, covering the luxemburg and orlicz norms, the duality theory of nfunctions, isomorphic containment of c 0 and. We also give concepts of orlicz spaces, weak orlicz spaces, orlicz sobolev spaces, weak orlicz sobolev spaces, orlicz morrey spaces and weak orlicz morrey spaces, orlicz lorentz spaces and weak orlicz lorentz spaces. In this theory, we introduce the definitions of orlicz spaces, weak orlicz spaces, orliczsobolev spaces, weak orliczsobolev spaces, orliczmorrey. For general terminology and results on orlicz spaces, see 1. To indicate reasons why classical as well as noncommutative orlicz spaces are emerging in the theory of classical and quantum physics the steady progress of physics requires for its theoretical formulation.
It follows from the theory of orlicz spaces 8, theorem. Banach function spaces is a very general class of banach spaces including all l p spaces for 1 p 1, orlicz spaces. A brief introduction to nfunctions and orlicz function spaces. Pdf on one class of orlicz functions semantic scholar. Gradient estimates in orlicz spaces for quasilinear. Since then, the theory of modulars and modular spaces is widely applied in the study of interpolation theory 22, 26 and various orlicz spaces 40. In particular, a series of martingale inequalities including the maximal function inequality in weak orlicz spaces are established. Lebesgue and sobolev spaces with variable exponent, or the general musielakorlicz spaces, the origins of which can be traced back to the work of orlicz in the 1930s. We also give concepts of orlicz spaces, weak orlicz spaces, orlicz sobolev spaces, weak orlicz sobolev spaces. Since then, the theory of the orlicztype spaces themselves has been well developed and these spaces have been widely used in many branches of analysis see, for example, 2, 25, 36, 29, 39.
The spaces are named for wladyslaw orlicz and zygmunt william birnbaum, who first defined them in 1931 besides the l p spaces, a variety of function spaces arising. Existence and multiplicity of solutions for a class of quasilinear problems in orliczsobolev spaces, complexe variables and elliptic equations 626 2017. In this theory, we introduce the definitions of orlicz spaces, weak orlicz spaces, orliczsobolev spaces, weak orliczsobolev spaces. In the theory of orlicz spaces, one defines the space. Rational approximation in orlicz spaces on carleson curves guven, ali and israfilov, daniyal m. The realvariable theory of function spaces has always been at.
Recently, motivated by certain questions in analysis, some more general musielakorlicz hardytype function spaces were introduced. This work is concerned with the existence and multiplicity of solutions for the following class of quasilinear problems. The aim of the project is to develop the general theory of continuous linear operators on orlicz bochner spaces, equipped with the socalled modular topology. This article concerns the existence of nontrivial weak solutions for a class of nonhomogeneous neumann. In this theory, we introduce the definitions of orlicz spaces, weak orlicz spaces, orlicz sobolev spaces, weak orlicz sobolev spaces, orlicz morrey.
Transfer principles and ergodic theory in orlicz spaces. It is a great honor to be asked to write this article for the proceedings of the conference. The aim of the project is to develop the general theory of continuous linear operators on orliczbochner spaces, equipped with the socalled modular. Realvariable theory of musielakorlicz hardy spaces. The realvariable theory of function spaces has always been at the core of harmonic analysis. Gradient estimates in orlicz spaces for quasilinear elliptic. Dec 11, 2019 in this paper, based on concepts of convex sets and convex functions, we introduce new concepts of functions, young functions, strong young functions and orlicz functions by relaxing definitions of functions, young functions, strong young functions, orlicz functions respectively. Buy orlicz spaces and modular spaces lecture notes in mathematics on free shipping on qualified orders.
Pdf applications of the theory of orlicz spaces to vector measures. Montgomerysmith department of mathematics, university of missouri, columbia, mo 65211. Pdf applications of the theory of orlicz spaces to. Orliczlorentz hardy martingale spaces pdf free download. Moreover, as a development of the theory of orlicz spaces, orliczhardy spaces and their dual.
In addition, by an interpolation theorem of boyd, they established an elliptic regularity result in orlicz sobolev spaces. There are two points i could not get well at proof of vallee poussins uniform integrablity theorem. Realvariable theory of musielakorlicz hardy spaces lecture. Apr 21, 2010 in this paper, the weak orlicz space wl. A general framework is introduced for the orliczbrunnminkowski theory that includes both the new addition and previously introduced concepts, and makes clear for the first time the relation to orlicz spaces and norms.
However, formatting rules can vary widely between applications and fields of interest or study. Just as orlicz spaces generalize l p spaces, the orlicz theory brings more generality, but presents additional challenges due to the loss of homogeneity. There have been many research activities concerning orlicz spaces see,, since it was introduced by w. Moreover, as a development of the theory of orlicz spaces, orliczhardy spaces and their dual spaces were studiedby stromberg42 and janson 27 on. Among other directions, the theory now addresses certain geometric properties of sets and the banach spaces that contain them. Note on linearity of rearrangementinvariant spaces soudsky, filip, annals of functional analysis, 2016. Moreover, we considered the have inclusion properties of orlicz spaces based on effects of the map references. Realvariable theory of musielakorlicz hardy spaces dachun. To have a generalization of this concept within the theory of orlicz spaces we need. We refer the reader to the monograph of roa and ren 22, corollary 4 on p. On applications of orlicz spaces to statistical physics.
Pdf regularity theory in orlicz spaces for elliptic. A general framework is introduced for the orlicz brunnminkowski theory that includes both the new addition and previously introduced concepts, and makes clear for the first time the relation to orlicz spaces and norms. Very recently, gardner, hug and weil 9 constructed a general framework for the orliczbrunnminkowski theory, and made clear for the rst time the relation to orlicz spaces and norms. Ive started to read raos theory of orlicz spaces book. Weak orlicz space and its applications to the martingale theory. Fixed point theory originally aided in the early developement of di erential equations. Weak compactness criteria in noncommutative orlicz spaces 3 spaces lg in terms of steklov functions may be found in 31, theorem 11. Search for library items search for lists search for contacts search for a library. Lebesgue and sobolev spaces with variable exponent, or the general musielak orlicz spaces, the origins of which can be traced back to the work of orlicz in the 1930s.
These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. The next section discusses the structure theory for subspaces of orlicz sequence spaces. The realvariable theory of function spaces has always been at the core. In recent years, progress towards an orlicz brunnminkowski theory is initiated by lutwak, yang, and zhang 23, 24 to initiate an extension of the brunnminkowski theory to an orlicz brunnminkowski theory. This article concerns the existence of nontrivial weak solutions for a class of nonhomogeneous neumann problems. Regularity theory in orlicz spaces for elliptic equations in reifenberg domains. Stanford libraries official online search tool for books, media, journals, databases, government documents and more. Orlicz space as eosw exponential orlicz space or simple ew with. Functional analysis answering to a recent question raised by lesnik, maligranda, and. We extend to orlicz spaces with weight a transfer principle of r. Indeed, the old seminal textbook by krasnoselskii and rutickii 1 1961 contains all the fundamental. Newest orliczspaces questions mathematics stack exchange. Fubini theorems for orlicz spaces 103 the orlicz spaces treated in this paper deviate from the classical orlicz spaces in that, instead of their being generated from the usual measure space, we shall generate them from a volume space and from the ensuing integration theory of bogdanowicz 1. Pointwise multipliers on musielakorlicz spaces nakai, eiichi, nihonkai mathematical journal, 2016.
The spaces are named for wladyslaw orlicz and zygmunt william birnbaum, who first defined them in 1931. Multiplicity of solutions for nonhomogeneous neumann problems in orlicz sobolev spaces shapour heidarkhani, massimiliano ferrara, giuseppe caristi, johnny henderson, amjad salari communicated by mokhtar kirane abstract. A brief introduction to nfunctions and orlicz function spaces john alexopoulos kent state university, stark campus march 12, 2004. To include a comma in your tag, surround the tag with double quotes. With this notation we can give the following interpretation of. In the 1950s, this study was carried on by nakano 19 who made the rst systematic study of spaces with variable exponent. Orliczaleksandrovfenchel inequality for orlicz multiple. They successively established the fundamental affine inequalities for. Weak orlicz space and its applications to the martingale. The main purpose of this book is to give a detailed and complete survey of recent progress related to the realvariable theory of musielakorlicz hardytype function spaces, and to lay the foundations for further applications. Martingale hardy spaces are widely studied in the field of mathematical physics and probability.