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Approximation in Orlicz-Slobodeckii space by functions in C[infinity] (Omega)

100%

Liskowski M.

Fasciculi Mathematici

1999

tom Nr 29

43-59

We wish to prove that [...] is dense in Orlicz-Slobodeckii space Bk.M (n) for some n c RN offinite measure.

Interpolation inequalities in Orlicz-Sobolev space

100%

Liskowski M.

Fasciculi Mathematici

1999

tom Nr 30

99-106

We consider the problem of detennining upper bounds for nonns of functions from Orlicz-Sobolev space[...], [...] in tenns of nonns of the space [...] and Orlicz space. The interpolation inequalities of this type are well-known for classical Sobolev spaces [...], [...]and also [1].

Density of smooth functions in Sobolev spaces "wth mixed functions"

100%

Liskowski M.

Fasciculi Mathematici

2014

tom Nr 53

77--83

The results presented in this paper concern approximation by smooth functions in the Sobolev spaces defined by means of a modular (1). These spaces can be a natural medium to study the partial differential equations with rapidly or slowly increasing coefficients (i.e. the coefficients are of a nonpolynomial type).

Approximation by functions in C0∞(Ω) in Orlicz - Sobolev spaces

100%

Liskowski M.

Fasciculi Mathematici

2005

tom Nr 36

73-82

The results presented in this paper concern the identity of spaces Wk, M Ω and Wk, M Ω generated by &phi-functions M with parameter for some class domains Ω ⊂ Rn and they are the extension of analogous results for clasical Sobolev spaces. The problem of approximation of elements in Wk, M Ω by smooth functions on various domains Ω ⊂ Rn were investigated by different authors for classic Sobolev spaces with integer values of k as well as for some generalization of Sobolev space to the case of noninteger values k (see e.g. N. Meyers and J. Serrin [11] in the case M(u) =up, p> 1; T. K. Donaldson and N. S. Trudinger [2], when M is arbitrary N-function; H. Hudzik [3], [4], [5], [6]. [7], when M is TV-function which depends on parameter; M. Liskowski [9] [10] for some family of generalized Orlicz-Sobolev space, when k is noninteger and M is N-function with parameter).

Sobolev spaces "with mixed functions"

100%

Liskowski M.

Fasciculi Mathematici

2012

tom Nr 48

73--82

This paper describes some generalization of modular function spaces Lϕψ defined by a modular Iϕѱ(f) = ∫baϕ (x, ∫dc ψ (y, f (x,y))dy) dx, ([3]). The next part of this paper focuses on using of spaces, defined previously, to introduce Sobolev spaces as a vector subspace of the generalized space Lϕѱ. Some selected properties of these spaces are presented.

Integral of function with values in complete modular space

100%

Liskowski M.

Demonstratio Mathematica

2002

tom Vol. 35, nr 2

347-356

The theorem on existence of an integral of a function with values in a modular space and some fundamental properties of this integral are given.

Matematyka w polskiej szkole u progu nowego stulecia

63%

Liskowska J. , Liskowski M.

Wiadomości Matematyczne

2011

tom T. 47, Nr 1

55-72

W niniejszym eseju scharakteryzowane zostały – podejmowane przez MEN i MNiSW – działania na rzecz poprawy efektywności kształcenia w polskim systemie edukacyjnym, ze szczególnym uwzglednieniem kształcenia matematycznego.