Inclusion between Morrey spaces and weak Morrey spaces


Hendra Gunawan


Institut Teknologi Bandung, Indonesia


Tue, 10/10/2017 - 12:00pm to 1:00pm


RC-4082, The Red Centre, UNSW


For $1\le p \le q<\infty$, we define the Morrey space $\mathcal{M}^p_q({\mathbb R}^n)$ to be the set of all $p$-locally integrable functions on ${\mathbb R}^n$ such that
\[ \| f \|_{{\mathcal M}^p_q} := \sup_{B \subset \mathbb{R}^n} |B|^{\frac{1}{q}-\frac{1}{p}} \left(\int_{B}|f(y)|^ \,dy\right)^\frac{1}{p}<\infty, \]
where the supremum is taken over all balls $B=B(a,r)$ in ${\mathbb R}^n$. By using the distribution function instead of the integral, one may also define the weak Morrey space $w{\mathcal M}^p_q({\mathbb R}^n)$. In this talk, I would like to discuss about the inclusion relation among Morrey spaces, as well as between Morrey spaces and weak Morrey spaces.

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