Littlewood paley theory and the study of function spaces pdf

For questions about the littlewoodpaley theory, a theoretical framework used to extend certain results about l2 functions to lp functions for 1 littlewood paley theory and the study of function spaces. The applications of the general theory to some wellknown function spaces are. The littlewoodpaley spaces provide a unified framework for the study of some important function. Let a e r, 98s be a regular sequence space and pdf be a. Littlewood paley theory and the study of function spaces by frazier, michael, 1956publication date 1991. We use this phrase to denote the study of squarefunction estimates in weighted lp and hardy spaces on irn, as well as the more general theory.

How does an operator t behave with respect to function spaces, e. Littlewood paley theory was developed to study function spaces in harmonic analysis and partial differential equations. Banach space of essentially bounded measurable functions on rn. Littlewoodpaley theory originated with the development of certain auxiliary integral ex pressions used in the study of analytic. Littlewoodpaley theory and function spaces with aloc. This is a result historically due to littlewood and paley, which explains the name. Littlewoodpaley theory for morrey spaces and their.

Next, we define some basic operations on function spaces which. Intoduction to pde 1 littlewoodpaley decomposition we start with a smooth, nonincreasing, radial nonnegative function. Littlewood paley theory and the study of function spaces cbms regional conference series in mathematics. Littlewood paley theory and the study of function spaces about this title. This paper intends to develop parallel tools for periodic functions. Outlineboundedness of operatorslittlewood paley theorymultipliers littlewood paley theorem proof. Citeseerx scientific documents that cite the following paper. Recently, it has contributed to the development of the \\varphi\transform and wavelet decompositions.

In this subsection we will consider a variant of the square function appearing at the righthand side of y where we replace the frequencyprojections j bybetterbehavedones. Destination page number search scope search text search scope search text. Littlewoodpaley theory for matrixweighted function spaces. Littlewoodpaley theory and multipliers george kinnear september 11, 2009. In harmonic analysis, a field within mathematics, littlewood paley theory is a theoretical framework used to extend certain results about l 2 functions to l p functions for 1 functions when p 2. Simple thresholding operations, applied in the unconditional basis, work essentially better for compressing, estimating, and recovering than they do in any other. Let denote a smooth function with the properties that is compactly supported in the intervals 4.

Request pdf littlewoodpaley theory for morrey spaces and their preduals zorko proved that morrey spaces are known to have preduals. We develop a geometric invariant littlewoodpaley theory for ar. Newest littlewoodpaleytheory questions mathematics. An orthogonal basis of l 2 which is also an unconditional basis of a functional space f is a kind of optimal basis for compressing, estimating, and recovering functions in f. Littlewoodpaley theory and the study of function spaces about this title.