123 research outputs found
Finite element approximation of the -Laplacian
We study a~priori estimates for the Dirichlet problem of the
-Laplacian,
We show that the gradients of the finite element approximation with zero
boundary data converges with rate if the exponent is
-H\"{o}lder continuous. The error of the gradients is measured in the
so-called quasi-norm, i.e. we measure the -error of
Interpolation in variable exponent spaces
In this paper we study both real and complex interpolation in the recently
introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also
take advantage of some interpolation results to study a trace property and some
pseudodifferential operators acting in the variable index Besov scale
Local Hardy Spaces of Musielak-Orlicz Type and Their Applications
Let \phi: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz) be a function such
that is an Orlicz function and (the class of local weights
introduced by V. S. Rychkov). In this paper, the authors introduce a local
Hardy space of Musielak-Orlicz type by the local grand
maximal function, and a local -type space
which is further proved to be the
dual space of . As an application, the authors prove
that the class of pointwise multipliers for the local
-type space ,
characterized by E. Nakai and K. Yabuta, is just the dual of
L^1(\rn)+h_{\Phi_0}(\mathbb{R}^n), where is an increasing function on
satisfying some additional growth conditions and a
Musielak-Orlicz function induced by . Characterizations of
, including the atoms, the local vertical and the local
nontangential maximal functions, are presented. Using the atomic
characterization, the authors prove the existence of finite atomic
decompositions achieving the norm in some dense subspaces of
, from which, the authors further deduce some
criterions for the boundedness on of some sublinear
operators. Finally, the authors show that the local Riesz transforms and some
pseudo-differential operators are bounded on .Comment: Sci. China Math. (to appear
On spaces based on the notion of a finitely additive integral
The article contains no abstrac
Absolute continuity of set functions with respect to a finitely subadditive measure
The article contains no abstrac
On some classes of finitely additive set functions
The article contains no abstrac
O szeregach doskonale zbieżnych w pewnych przestrzeniach funkcyjnych
The article contains no abstrac
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