public class ActivityName extends AppCompatActivity implements SearchView.OnQueryTextListener {

    @Override
    public boolean onCreateOptionsMenu(Menu menu) {
        getMenuInflater().inflate(R.menu.menu_main, menu);

        MenuItem item = menu.findItem(R.id.action_search);
        SearchView searchview = new SearchView(this);
        SearchManager searchManager = (SearchManager) getSystemService(SEARCH_SERVICE);
        searchview.setSearchableInfo(searchManager.getSearchableInfo(getComponentName()));
        ...
        MenuItemCompat.setShowAsAction(item, 
                MenuItemCompat.SHOW_AS_ACTION_COLLAPSE_ACTION_VIEW | 
                MenuItemCompat.SHOW_AS_ACTION_IF_ROOM);
        MenuItemCompat.setActionView(item, searchview);
        searchview.setOnQueryTextListener(this);
        searchview.setIconifiedByDefault(false);

        return super.onCreateOptionsMenu(menu);
    }

    private void changeSearchViewTextColor(View view) { ... }

    @Override
    public boolean onQueryTextSubmit(String query) { return false; }

    @Override
    public boolean onQueryTextChange(String newText) {
        // update the observer here (aka nested fragments)
        return true;
    }
}

private ArrayList<String> originalList; // I used String objects in my tests
private ArrayList<String> filteredList;
private ListFilter filter = new ListFilter();

@Override
public int getCount() {
    return filteredList.size();
}

public Filter getFilter() {
    return filter;
}

private class ListFilter extends Filter {
    @Override
    protected FilterResults performFiltering(CharSequence constraint) {
        FilterResults results = new FilterResults();
        if (constraint != null && constraint.length() > 0) {
            constraint = constraint.toString().toLowerCase();
            final List<String> list = originalList;
            int count = list.size();

            final ArrayList<String> nlist = new ArrayList<>(count);
            String filterableString;
            for (int i = 0; i < count; i++) {
                filterableString = list.get(i);
                if (filterableString.toLowerCase().contains(constraint)) {
                    nlist.add(filterableString);
                }
            }

            results.values = nlist;
            results.count = nlist.size();
        } else {
            synchronized(this) {
                results.values = originalList;
                results.count = originalList.size();
            }
        }
        return results;
    }

    @SuppressWarnings("unchecked")
    @Override
    protected void publishResults(CharSequence constraint, FilterResults results) {
        if (results.count == 0) {
            notifyDataSetInvalidated();
            return;
        }

        filteredList = (ArrayList<String>) results.values;
        notifyDataSetChanged();
    }
}

private static ActivityName instance;
private FilterManager filterManager;

@Override
protected void onCreate(Bundle savedInstanceState) {
    ...
    instance = this;
    filterManager = new FilterManager();
}

public static FilterManager getFilterManager() {
    return instance.filterManager; // return the observable class
}

@Override
public boolean onQueryTextChange(String newText) {
    filterManager.setQuery(newText); // update the observable value
    return true;
}

public class FilterManager extends Observable {
    private String query;

    public void setQuery(String query) {
        this.query = query;
        setChanged();
        notifyObservers();
    }

    public String getQuery() {
        return query;
    }
}

private ViewPager pager;
private ViewPagerAdapter pagerAdapter;

@Override
public View onCreateView(...) {
    ...
    pagerAdapter = new ViewPagerAdapter(
         getActivity(),                    // pass the context,
         getChildFragmentManager(),        // the fragment manager
         MainActivity.getFilterManager()   // and the filter manager
    );
}

public class ViewPagerAdapter extends FragmentStatePagerAdapter {

    private Context context;
    private FilterManager filterManager;

    public ViewPagerAdapter(FragmentManager fm) {
        super(fm);
    }

    public ViewPagerAdapter(Context context, FragmentManager fm, 
               FilterManager filterManager) {
        super(fm);
        this.context = context;
        this.filterManager = filterManager;
    }

    @Override
    public Fragment getItem(int i) {
        NestedFragment fragment = new NestedFragment(); // see (*)
        filterManager.addObserver(fragment); // add the observer
        return fragment;
    }

    @Override
    public int getCount() {
        return 10;
    }

    @Override
    public void destroyItem(ViewGroup container, int position, Object object) {
        NestedFragment fragment = (NestedFragment) object; // see (*)
        filterManager.deleteObserver(fragment); // remove the observer
        super.destroyItem(container, position, object);
    }
}

public class NestedFragment extends Fragment implements Observer {
    private boolean listUpdated = false; // init the update checking value
    ...
    // setup the listview and the list adapter
    ...
    // use onResume to filter the list if it's not already done
    @Override
    public void onResume() {
        super.onResume();
        // get the filter value
        final String query = MainActivity.getFilterManager().getQuery();
        if (listview != null && adapter != null 
                     && query != null && !listUpdated) {
            // update the list with filter value
            listview.post(new Runnable() {
                @Override
                public void run() {
                    listUpdated = true; // set the update checking value
                    adapter.getFilter().filter(query);
                }
            });
        }
    }
    ...
    // automatically triggered when setChanged() and notifyObservers() are called
    public void update(Observable obs, Object obj) {
        if (obs instanceof FilterManager) {
            String result = ((FilterManager) obs).getQuery(); // retrieve the search value
            if (listAdapter != null) {
                listUpdated = true; // set the update checking value
                listAdapter.getFilter().filter(result); // filter the list (with #2)
            }
        }
    }
}

@Override
public Fragment getItem(int index) {
    Fragment frag = null;
    switch (index) {
        case 0:
            frag = new FirstNestedFragment();
            break;
        case 1:
            frag = new SecondFragment();
            break;
        ...
    }
    return frag;
}

@Override
public Object instantiateItem(ViewGroup container, int position) {
    ObserverFragment fragment = 
            (ObserverFragment) super.instantiateItem(container, position);
    filterManager.addObserver(fragment); // add the observer
    return fragment;
}

@Override
public void destroyItem(ViewGroup container, int position, Object object) {
    filterManager.deleteObserver((ObserverFragment) object); // delete the observer
    super.destroyItem(container, position, object);
}

public class ObserverFragment extends Fragment implements Observer {
    public void update(Observable obs, Object obj) { /* do nothing here */ }
}

public class FirstNestedFragment extends ObserverFragment {
    @Override
    public void update(Observable obs, Object obj) { }
}