You need to look at what the license of your API will be.

Looking at the [ArcGIS Copyright Information page][1]...

> ...No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system, except as expressly permitted in writing by ESRI...

Therefore, using the api and allowing open source freedoms, such as reproduction and distribution is asking for trouble.

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Therefore, to answer your question, you need to look at the nature of your "referenced libraries". You need to look at their copyright/licensing terms, analyze them, and determine how they will impact the goals of your project. In the end, you will know your work is Open Source, if it meets their [definition][2]:

> 1. Free Redistribution
> 2. Source Code
> 3. Derived Works
> 4. Integrity of The Author's Source Code
> 5. No Discrimination Against Persons or Groups
> 6. No Discrimination Against Fields of Endeavour
> 7. Distribution of License
> 8. License Must Not Be Specific to a Product
> 9. License Must Not Restrict Other Software
> 10. License Must Be Technology-Neutral

 [1]: http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?TopicName=copyright%20information
 [2]: http://opensource.org/osd-annotated