Wyniki wyszukiwania

1

Erratum to "A class of Fourier multipliers on H¹(ℝ²)" (Studia Math. 140 (2000), 289-298)

100%

Wojciechowski M.

Studia Mathematica

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2002

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tom 152

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nr 1

103-104

2

Translation invariant projections in Sobolev spaces on tori in the L¹ and uniform norms

100%

Wojciechowski M.

Studia Mathematica

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1991

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tom 100

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nr 2

149-167

EN

The idempotent multipliers on Sobolev spaces on the torus in the L¹ and uniform norms are characterized in terms of the coset ring of the dual group of the torus. This result is deduced from a more general theorem concerning certain translation invariant subspaces of vector-valued function spaces on tori.

3

Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections

100%

Wojciechowski M.

Studia Mathematica

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1993

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tom 104

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nr 2

181-193

EN

We characterize those anisotropic Sobolev spaces on tori in the $L^1$ and uniform norms for which the idempotent multipliers have a description in terms of the coset ring of the dual group. These results are deduced from more general theorems concerning invariant projections on vector-valued function spaces on tori. This paper is a continuation of the author's earlier paper [W].

4

Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm

64%

Pełczyński A., Wojciechowski M.

Studia Mathematica

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1993

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tom 107

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nr 1

61-100

EN

Let E be a Banach space. Let $L¹_{(1)}(ℝ^d,E)$ be the Sobolev space of E-valued functions on $ℝ^d$ with the norm $ʃ_{ℝ^d} ∥f∥_E dx + ʃ_{ℝ^d} ∥∇f∥_E dx = ∥f∥₁ + ∥∇f∥₁$. It is proved that if $f ∈ L¹_{(1)}(ℝ^d,E)$ then there exists a sequence $(g_m) ⊂ L_{(1)}¹(ℝ^d,E)$ such that $f = ∑_m g_m$; $∑_m (∥g_m∥₁ + ∥∇g_m ∥₁) < ∞$; and $∥g_m∥_∞^{1/d} ∥g_m∥₁^{(d-1)/d} ≤ b∥∇g_m∥₁$ for m = 1, 2,..., where b is an absolute constant independent of f and E. The result is applied to prove various refinements of the Sobolev type embedding $L_{(1)}¹(ℝ^d,E) ↪ L²(ℝ^d,E)$. In particular, the embedding into Besov spaces $L¹_{(1)} (ℝ^d,E) ↪ B_{p,1}^{θ(p,d)}(ℝ^d,E)$ is proved, where $θ(p,d) = d(p^{-1} + d^{-1} -1)$ for 1 < p ≤ d/(d-1), d=1,2,... The latter embedding in the scalar case is due to Bourgain and Kolyada.

5

Non-uniqueness of topology for algebras of polynomials

64%

Wojciechowski M., Żelazko W.

Colloquium Mathematicum

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1997

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tom 72

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nr 1

111-121

Ograniczanie wyników

4 Studia Mathematica

1 Colloquium Mathematicum

5 Wojciechowski M.

1 Pełczyński A.

1 Żelazko W.

1 2002

1 1997

2 1993

1 1991

Erratum to "A class of Fourier multipliers on H¹(ℝ²)" (Studia Math. 140 (2000), 289-298)

Translation invariant projections in Sobolev spaces on tori in the L¹ and uniform norms

Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections

Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm

Non-uniqueness of topology for algebras of polynomials