\renewcommand{\L}[1]{\mathcal{L}^{#1}}
\newcommand{\set}[1]{\left\{#1\right\}}
\newcommand{\abs}[1]{\left|#1\right|}
\newcommand{\brac}[1]{\left(#1\right)}
\newcommand{\sqbrac}[1]{\left[#1\right]}
\newcommand{\lbrac}[1]{\left\langle#1\right\rangle}
\newcommand{\nm}[1]{\lVert#1\rVert}
\newcommand{\bnm}[1]{\big\Vert#1\big\Vert}
\newcommand{\R}{\mathbb{R}}
\newcommand{\RR}{\mathcal{R}}
\newcommand{\HH}{\mathcal{H}}
\newcommand{\B}{\mathcal{B}}
\newcommand{\iog}{\rm{iog}}
\newcommand{\OO}{\mathcal{O}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\D}{\mathbb{D}}
\newcommand{\T}{\mathbb{T}}
\newcommand{\deriv}[2]{\frac{\mathrm{d}#1}{\mathrm{d}#2}}
\newcommand{\pderiv}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\DD}{\widehat{\mathcal{D}}}
\newcommand{\HO}{\mathcal{H}}
\renewcommand{\Re}{\hspace{0.06cm}\textrm{Re}\hspace{0.12cm}}

\newcommand{\LMOA}{\textnormal{LMOA}}
\def\VMOA{\mathord{\textnormal{VMOA}}}
\def\BMOA{\mathord{\textnormal{BMOA}}}
\def\a{\alpha}       \def\b{\beta}        \def\g{\gamma}
\def\d{\delta}       \def\De{{\Delta}}    \def\e{\varepsilon}
\def\la{\lambda}     \def\om{\omega}      \def\O{\Omega}
\def\s{\sigma}       \def\t{\theta}       \def\f{\phi}
\def\p{\psi}         \def\r{\rho}         \def\z{\zeta}
\def\F{\Phi}         \def\c{\chi}         \def\vp{\varphi}
\def\omh{\widehat{\omega}}
\def\l{\left}
\def\ri{\right}
\def\discalg{\mathcal{A}}
\def\hw{H_\omega^\infty}
\def\hwh{H_{\widehat{\omega}}^\infty}
\def\fw{\|f\|_{H_\omega^\infty}}
\def\fwr{\|f_r\|_{H_\omega^\infty}}
\def\gwr{\|g_r\|_{H_\omega^\infty}}
\def\ph{\hat{p}}
\newcommand{\hstar}[1]{H_{\omega,\star,#1}^{\infty}}

%\newtheorem{theorem}{Theorem}[section]
%\newtheorem{conjecture}{Conjecture}[section]
%\newtheorem{lemma}{Lemma}[section]
%\newtheorem{proposition}{Proposition}[section]
%\newtheorem{corollary}{Corollary}[section]
%\newtheorem{definition}{Definition}[section]

\theoremstyle{definition}
\newtheorem{defi}{Definition}
\theoremstyle{definition}
\newtheorem{ques}{Question}
\theoremstyle{plain}
\newtheorem{theo}{Theorem}[section]
\newtheorem{conj}{Conjecture}
\theoremstyle{plain}
\newtheorem{prop}[theo]{Proposition}
\theoremstyle{plain}
\newtheorem{lem}[theo]{Lemma}
\theoremstyle{plain}
\newtheorem{coro}[theo]{Corollary}
\theoremstyle{definition}
\newtheorem{exa}[theo]{Example}
\theoremstyle{definition}
\newtheorem{prob}[theo]{Problem}
\theoremstyle{definition}
\newtheorem{rema}{Remark}
\numberwithin{defi}{chapter}
\numberwithin{ques}{chapter}
\numberwithin{theo}{chapter}
\numberwithin{conj}{chapter}
%\numberwithin{prop}{section}
%\numberwithin{lem}{section}
%\numberwithin{coro}{section}
%\numberwithin{exa}{section}
%\numberwithin{prob}{section}
%\numberwithin{rema}{section}

\theoremstyle{plain}
\newtheorem{lettertheorem}{Theorem}%asdf
\renewcommand{\thelettertheorem}{\Alph{lettertheorem}}%asdf

\theoremstyle{plain}
\newtheorem{letterlemma}{Lemma}
\renewcommand{\theletterlemma}{\Alph{letterlemma}}


\newenvironment{pro}
{\noindent{\it Proof. }}{\hfill $\Box$\par\vspace{2.5mm}}
\newenvironment{solu}
{\noindent{\it Solution. }}{\hfill} 