On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz

Stein, Elias M.

doi:10.1090/s0002-9947-1958-0112932-2

Cited by 324 publications

(93 citation statements)

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“…That this operator also satisfies (1) was first proved by Zygmund in 1944. As a generalization of the Marcinkiewicz operator to higher dimensions, Stein [14] proposed the choice…”

Section: Introductionmentioning

confidence: 99%

Weighted inequalities for rough square functions through extrapolation

Duoandikoetxea

Seijo

2002

Studia Math.

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Abstract. Weighted inequalities for some square functions are studied. L 2 results are proved first using the particular structure of the operator and then extrapolation of weights is applied to extend the results to other L p spaces. In particular, previous results for square functions with rough kernel are obtained in a simpler way and extended to a larger class of weights. Introduction. Littlewood-Paley and Marcinkiewicz type operatorsare given by square functions. For a historical overview of this topic and its several aspects the reader can consult the paper by E. Stein [15]. A typical case is the following: given a function N in R n satisfying appropriate conditions, define N t (x) = t −n N (t −1 x) for t > 0 and construct the square function

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“…That this operator also satisfies (1) was first proved by Zygmund in 1944. As a generalization of the Marcinkiewicz operator to higher dimensions, Stein [14] proposed the choice…”

Section: Introductionmentioning

confidence: 99%

Weighted inequalities for rough square functions through extrapolation

Duoandikoetxea

Seijo

2002

Studia Math.

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“…When D 1; we shall denote 1 simply by ˝: The area of the Marcinkiewcz integrals have been under intensive research. This operator ˝w as first introduced by Stein in [15]. He proved that if2…”

Section: Introduction and Resultsmentioning

confidence: 99%