Inequality about holomorphic functions on the disk
51659
If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
89050
If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function.
8039
an analytic function from unit disk to unit disk with two fixed point
137971
Existence of an holomorphic function
110219
Bound on the derivative of a holomorphic function at $0$
110771
Schwarz's Lemma and functions with positive real part
87723
Show a holomorphic function on unit disc with with $|f'(z) - f'(0)| < |f'(0)|$ is injective
94680
Holomorphic function $f$ such that $f'(z_0) \neq 0$
83014
Holomorphic function interpolating $e^{-n}$
137045
The estimate of real and imaginary part of a holomorphic function
115863
Every harmonic function is the real part of a holomorphic function
114488
If $|f|+|g|$ is constant on $D,$ prove that holomorphic functions $f,~g$ are constant on $D$.
82625
How do I prove this using question using Cauchy-Schwarz inequality?
44458
Uniform limit of holomorphic functions
19750
If a function $f$ is holomorphic on the closed unit disk centered at the origin and is real valued whenever $|z| = 1$, then $f$ is constant.
23585
Show that a holomorphic function satisfying $|f(z)|\leq c|z|^n$ must be $f(z)=a\cdot z^n$ for some a.
100608
Prove that $\|v\|_{H^1(\Omega )}\leq C(\|f\|_{L^2(\Omega )}+\|v\|_{H^{1/2}(\partial \Omega )}+\|\partial _\nu v\|_{H^{1/2}(\partial \Omega )}))$