Conjugate Functions in Orlicz Spaces

Ryan, R. S.

doi:10.21236/ad0295706

Cited by 19 publications

(13 citation statements)

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“…For the Hilbert transform and the conjugate function the analogous problem was solved in [21], [22], [23] iii) ^ € A2 and t^° is quasi-convex for some a 6 (0,1).…”

Section: Jmmentioning

confidence: 99%

Weighted Estimates for Classical Integral Operators

Kokilashvili¹

1990

Nonlinear Analysis, Function Spaces and Applications Vol. 4

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“…For the Hilbert transform and the conjugate function the analogous problem was solved in [21], [22], [23] iii) ^ € A2 and t^° is quasi-convex for some a 6 (0,1).…”

Section: Jmmentioning

confidence: 99%

Weighted Estimates for Classical Integral Operators

Kokilashvili¹

1990

Nonlinear Analysis, Function Spaces and Applications Vol. 4

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“…Theories of harmonic analysis, and in particular Hardy spaces, which use norms more general than those of the Lebesgue L p spaces have a long history [19,3,14,15,7,8,16,23,20,11,12,21,1,2]. Although we are concerned here with spaces which behave like L 1 under the action of maximal operators and singular integrals there would be nothing to gain by restricting the remarks which follow to that setting.…”

Section: Spaces With Rearrangement-invariant Normsmentioning

confidence: 99%

On the Duality of Hardy Spaces NearH1

Lowe

1996

Journal of Functional Analysis

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“…Then equation (8) and replace u + 2hir in the denominator with (2A + 2)n, there is an error (10). t>(5r/A;/fr>) f(V«;/f))…”

Section: Jir/nmentioning

confidence: 99%

“…For/ G L%, Ryan [10] has shown \\Sn(f)\\* < cll/ll<j» wnere c is independent of n and/if and only if L% is reflexive. Suppose Tn(x) is an nth degree trigonometric polynomial of best approximation to / and define E"(f\=\\f(x) -Tn(x)l.…”

Section: J -Mrmentioning

confidence: 99%

On the degree of approximation of a function by the partial sums of its Fourier series

Cohen¹

1978

Trans. Amer. Math. Soc.

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Abstract. When / is a lit periodic function with rth order fractional derivative, r > 0, of /»-bounded variation, Golubov has obtained estimates of the degree of approximation of/, in the L* norm, q > p, by the partial sums of its Fourier series. Here we consider the analogous problem for functions whose fractional derivatives are of ^-bounded variation and obtain estimates of the degree of approximation.in an Orlicz space norm. In a similar manner we shall extend various results that he obtained on degree of approximation in the sup norm. §1Let/be a real function of period 2tt. If the rth fractional derivative, r > 0, is of bounded/?-variation, Golubov [3] has obtained estimates of the degree of approximation of/, in the sup and Lq norms, q > /?, by the partial sums of the Fourier series offWe consider the analogous problem for functions whose fractional derivatives are of ^-bounded variation. In 2.1 we extend Salem's theorem of uniform convergence of Fourier series. In 2.2 we obtain estimates on the degree of approximation in an Orlicz space norm.In this chapter we shall review the background material which we shall require. In § 1 we concern ourselves with Orlicz spaces, §2 will present basic information on cp-bounded variation, and §3 contains the relevant information on the fractional integral and derivative.

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Conjugate Functions in Orlicz Spaces

Cited by 19 publications

References 0 publications

Weighted Estimates for Classical Integral Operators

Weighted Estimates for Classical Integral Operators

On the Duality of Hardy Spaces NearH1

On the degree of approximation of a function by the partial sums of its Fourier series

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