How much of the underwater land masses within the arctic ocean is considered continental shelf?
Yool &amp; Fasham in An Examination of the Continental shelf pump in an open ocean general circulation model Global Biogeochemical Cycles Volume 15, Issue 4, pages 831–844, divide the continental shelves into 32 named regions (see Fig. 2), and give areas for each (see table 1).  

The regions that are completely in the arctic ocean are:

Russian arctic shelf 1,503,000 sq. km. 

Siberian arctic shelf 1,825,000 sq. km. 

North American arctic shelf 498,000 sq. km. 

There are three other regions that are partially in the arctic ocean, 

Iceland and Greenland shelf, North Sea shelf, and Berring Sea shelf, but looking at Fig. 2 and table 1 these seem like small contributors. 

Roughly 4 million sq. km total.