Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $p\in(1,\infty)$. Assume that we have a sequence of functions $\{f_i:i\in\mathbb{N}\}\subset L^p(\mathbb{R}^n)$ such that $$ \left(\sum\limits_{i=1}^\infty|f_i|^2\right)^{\frac{1}{2}}\in L^p(\mathbb{R}^n)\qquad \{\mu (f_i):i\in\mathbb{N}\}\subset L^p(\mathbb{R}^n) $$ I want to prove that $$ \left\Vert\left(\sum\limits_{i=1}^\infty|\mu(f_i)|^2\right)^{\frac{1}{2}}\right\Vert_p \leq A_p\left\Vert\left(\sum\limits_{i=1}^\infty|f_i|^2\right)^{\frac{1}{2}}\right\Vert_p $$ Here we can assume that $\mu$ is the Hardy-Littlewood's maximal operator (centered or non-centered).

share|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.