Bernstein and Steckin inequalities play an important role in approximation theory.For example,Bernstein inequality is the main tool to prove the Inverse Theorem and Embedding Theorem.This paper establishes the relation between weighted Bernstein-type inequality and Steckin-type inequality in a general system of multivariate function.%Bernstein不等式在三角多项式逼近中起着非常重要的作用,比如它是证明逼近论逆定理即Steckin不等式的主要工具.文章建立了多维加权Bernstein型不等式与Steckin型不等式的关系,并进一步给出若干应用.
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