Weighted Inequalities in Fourier Analysis

Heinig, H. P.

doi:10.1007/978-3-663-01272-6_2

Cited by 16 publications

(16 citation statements)

References 13 publications

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“…One can show that an easy modification of ideas used in [3] provides the following result which generalizes that of [3] (for notation see below).…”

Section: ])mentioning

confidence: 87%

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Weighted inequalities for geometric means

Opic¹,

Gurka²

1994

Proc. Amer. Math. Soc.

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“…One can show that an easy modification of ideas used in [3] provides the following result which generalizes that of [3] (for notation see below).…”

Section: ])mentioning

confidence: 87%

“…In our method some ideas from [5][6][7]3] are employed. Let us point out that "the method of differential equations" is used here for the first time in the context of the geometric mean operator.…”

Section: ])mentioning

confidence: 99%

Weighted inequalities for geometric means

Opic¹,

Gurka²

1994

Proc. Amer. Math. Soc.

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“…in Theorem 4.1 we get the results for operators Aafix) = ^lofiy)y^' <f^-x^Tñy)V^- (4) Define w £ B^ iff / log-w(x) < C w.…”

mentioning

confidence: 66%

“…It is thus of interest to characterize the weights w : E+ -> R+ for which (1.2) IIVllp.«^C||/||pflB, as this gives extensions of the classical norm inequalities. This is the reason why the study of (1.2) has recently attracted a great deal of attention [3,4,[6][7][8][9], beginning with [1] Ariño and Muckenhoupt for the averaging operator Af(x) = j¿ fo f to the more general version of [3] for operators of the type S<j>f(x) = /0 <p(t)f(tx)dt. All of these operators are special cases of (1.1).…”

Section: Introductionmentioning

confidence: 99%