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Displaying 141 – 160 of 3651

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A note on integer translates of a square integrable function on ℝ

Maciej Paluszyński (2010)

Colloquium Mathematicae

We consider the subspace of L²(ℝ) spanned by the integer shifts of one function ψ, and formulate a condition on the family ψ ( · - n ) n = - , which is equivalent to the weight function n = - | ψ ̂ ( · + n ) | ² being > 0 a.e.

A note on multilinear Muckenhoupt classes for multiple weights

Songqing Chen, Huoxiong Wu, Qingying Xue (2014)

Studia Mathematica

This paper is devoted to investigating the properties of multilinear A P conditions and A ( P , q ) conditions, which are suitable for the study of multilinear operators on Lebesgue spaces. Some monotonicity properties of A P and A ( P , q ) classes with respect to P⃗ and q are given, although these classes are not in general monotone with respect to the natural partial order. Equivalent characterizations of multilinear A ( P , q ) classes in terms of the linear A p classes are established. These results essentially improve and extend...

A note on rare maximal functions

Paul Alton Hagelstein (2003)

Colloquium Mathematicae

A necessary and sufficient condition is given on the basis of a rare maximal function M l such that M l f L ¹ ( [ 0 , 1 ] ) implies f ∈ L log L([0,1]).

A note on rearrangements of Fourier coefficients

Hugh L. Montgomery (1976)

Annales de l'institut Fourier

Let f ( x ) Σ a n e 2 π i n x , f * ( x ) n = 0 a * n cos 2 π n x , where the a * n are the numbers | a n | rearranged so that a n * 0 . Then for any convex increasing ψ , ψ ( | f | 2 1 ψ ( 20 | f * | 2 1 . The special case ψ ( t ) = t q / 2 , q 2 , gives f q 5 f * q an equivalent of Littlewood.

A note on some expansions of p-adic functions

Grzegorz Szkibiel (1992)

Acta Arithmetica

Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by ( ϕ ) m . The system ( ϕ ) m is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to ( ϕ ) m . This paper is a remark to Rutkowski’s paper. We define another system ( h ) n in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski. The system...

A note on the convolution theorem for the Fourier transform

Charles S. Kahane (2011)

Czechoslovak Mathematical Journal

In this paper we characterize those bounded linear transformations T f carrying L 1 ( 1 ) into the space of bounded continuous functions on 1 , for which the convolution identity T ( f * g ) = T f · T g holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.

A note on the strong maximal operator on ℝⁿ

Jiecheng Chen, Xiangrong Zhu (2004)

Studia Mathematica

We prove that for f ∈ L ln⁺L(ℝⁿ) with compact support, there is a g ∈ L ln⁺L(ℝⁿ) such that (a) g and f are equidistributed, (b) M S ( g ) L ¹ ( E ) for any measurable set E of finite measure.

Currently displaying 141 – 160 of 3651