MathDB

For a real-valued function

f(x,y)

of two positive real variables

x

and

y

, define

f

to be linearly bounded if and only if there exists a positive number

K

such that

|f(x,y)| < K(x+y)

for all positive

x

and

y.

Find necessary and sufficient conditions on the real numbers

\alpha

and

\beta

such that

x^{\alpha}y^{\beta}

is linearly bounded.

Problem Statement