This is not meant to address tax implications, solely the implications of working in Canada while under another type of permit.
Working remotely for a company located outside of Canada, where the worker is also remunerated outside of Canada, is not considered to be work for the purposes of requiring a work permit. See the section labeled 'What kind of activities are not considered to be "work"?' on Immigration, Refugees and Citizenship Canada's website. I have also confirmed this interpretation with the CIC officer at the nearest border crossing.
The wrinkle in your case would be you saying it is your "own" company. It basically comes down to whether you are competing with Canadians and therefore impacting the labour market. Are you the only employee of your company? Presumably in that case you are not impacting the labour market because there is no market for additional employees, at least outside the US (assuming that is true). Are you competing with Canadians? It depends on how you find work, and whether those customers are located in the US, Canada or elsewhere.