Composition operator for functions of bounded variation

Composition operator into the space of function of bounded variation

Let $Ω_1, Ω_2\subset \mathbb R^n$ and $1\leq p <\infty$. We study the optimal conditions on a homeomorphism $f:Ω_1$ onto $Ω_2$ which guarantee that the composition $u\circ f$ belongs to the space $BV(Ω_1)$ for every $u\in W^{1,p}(Ω_2)$. We show that the sufficient and necessary condition is an existence of a function $K(y)\in L^{p'}(Ω_2)$ such that $|Df|(f^{-1}(A))\leq \int_A K(y)\,dy$ for all Borel sets $A$.

有界广义变差函数的二重Fourier-Legendre函数项级数的一致收敛性

Uniform Convergence of Double Fourier-Legendre series of Functions of Bounded Generalized Variation

研究了有界调和变差函数和有界部分$Λ$ -变差函数的二重Fourier-Legendre级数的一致收敛性.

关于有界部分广义变差函数的二重傅里叶级数的收敛性

On the convergence of double Fourier series of functions of bounded partial generalized variation

研究了有界部分$Λ$ -变差函数的二重傅里叶级数的收敛性.给出了有界部分$Λ$ -变差函数的傅里叶级数收敛的序列$Λ=\{λ_n\}$的充分必要条件。

Composition operators on Hardy-Sobolev spaces and $BMO$-quasiconformal mappings

In this paper we consider composition operators on Hardy-Sobolev spaces in connections with $BMO$-quasiconformal mappings. Using the duality of Hardy spaces and $BMO$-spaces we prove that $BMO$-quasiconformal mappings generate bounded composition operators from Hardy-Sobolev spaces to Sobolev spaces.

有界广义变差函数的双重Walsh-傅里叶级数的收敛性与可和性

On the Convergence and Summability of double Walsh-Fourier series of functions of bounded generalized variation

研究了有界广义变差函数的二重Walsh-傅里叶级数的负阶部分和及Cesáro平均的收敛性.

关于有界部分广义变分函数的多重傅里叶级数的收敛性

On the convergence of multiple Fourier series of functions of bounded partial generalized variation

研究了有界部分$% Λ$ -变差函数的多重傅里叶级数的收敛性。给出了有界部分$Λ$ -变差函数的多重傅里叶级数收敛的序列$Λ=\{λ_n\}$的充分必要条件.