Wyniki wyszukiwania

1

A class of Fourier multipliers on H¹(ℝ²)

100%

Wojciechowski M.

Studia Mathematica

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2000

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tom 140

|

nr 3

289-298

EN

An integral criterion for being an $H^1(ℝ^2)$ Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.

2

A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains

100%

Wojciechowski M.

Studia Mathematica

|

2000

|

tom 140

|

nr 3

273-287

EN

It is proved that if $m : ℝ^d → ℂ$ satisfies a suitable integral condition of Marcinkiewicz type then m is a Fourier multiplier on the $H^1$ space on the product domain $ℝ^{d_1}×...×ℝ^{d_k}$. This implies an estimate of the norm $N(m,L^p(ℝ^d)$ of the multiplier transformation of m on $L^p(ℝ^d)$ as p→1. Precisely we get $N(m,L^p(ℝ^d))≲(p-1)^{-k}$. This bound is the best possible in general.

3

On the relationships between Fourier-Stieltjes coefficients and spectra of measures

63%

Ohrysko P., Wojciechowski M.

Studia Mathematica

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2014

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tom 221

|

nr 2

117-140

EN

We construct examples of uncountable compact subsets of complex numbers with the property that any Borel measure on the circle group with Fourier coefficients taking values in this set has a natural spectrum. For measures with Fourier coefficients tending to 0 we construct an open set with this property. We also give an example of a singular measure whose spectrum is contained in our set.

Ograniczanie wyników

3 Studia Mathematica

3 Wojciechowski M.

1 Ohrysko P.

1 2014

2 2000

A class of Fourier multipliers on H¹(ℝ²)

A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains

On the relationships between Fourier-Stieltjes coefficients and spectra of measures