I want to show that $\sum_{|\alpha||,|\beta|\leq N}sup\{t^{\alpha}D^{\beta}(x_1-t_1)_{+}^{N+1}\cdot\cdot\cdot(x_n-t_n)^{N+1}_{+}|t_i>0 \text{ for all i=1,...,n}\} $ is bounded by something in the form of $C(1+|x|)^M$.

Here $x=(x_1,...,x_n)\in \mathbb{R}^n$ and $x_i>0$ for all $i$ and $\alpha, \beta$ are multi indices. $D^{\beta}=(-1)^{|\beta|}\partial_1^{\beta_1}\cdot\cdot\cdot\partial_n^{\beta_n}$ where $\partial_i=\frac{\partial}{\partial x_i}$.Also, $(x_1)_+=max\{x_1,0\}$

I have tried many things but have failed miserable. Any help is appreciated. Thank you!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.